3,020 results on '"Moment-generating function"'
Search Results
2. A New Extension of the Exponentiated Weibull–Poisson Family Using the Gamma-Exponentiated Weibull Distribution: Development and Applications.
- Author
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Chaisee, Kuntalee, Khamkong, Manad, and Paksaranuwat, Pawat
- Subjects
- *
DISTRIBUTION (Probability theory) , *WEIBULL distribution , *PARAMETER estimation , *HAZARD function (Statistics) , *SURVIVAL rate - Abstract
This study proposes a new five-parameter distribution called the gamma-exponentiated Weibull–Poisson (GEWP) distribution. As an extension of the exponentiated Weibull–Poisson family, the GEWP distribution offers a more flexible tool for analyzing a wider variety of data due to its theoretically and practically advantageous properties. It encompasses established distributions like the exponential, Weibull, and exponentiated Weibull. The development of the GEWP distribution proposed in this paper is obtained by combining the gamma–exponentiated Weibull (GEW) and the exponentiated Weibull–Poisson (EWP) distributions. Therefore, it serves as an extension of both the GEW and EWP distributions. This makes the GEWP a viable alternative for describing the variability of occurrences, enabling analysis in situations where GEW and EWP may be limited. This paper analyzes the probability distribution functions and provides the survival and hazard rate functions, the sub-models, the moments, the quantiles, and the maximum likelihood estimation of the GEWP distribution. Then, the numerical experiments for the parameter estimation of GEWP distribution for some finite sample sizes are presented. Finally, the comparative study of GEWP distribution and its sub-models is investigated via the goodness of fit test with real datasets to illustrate its potentiality. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
3. Some Comments about the p-Generalized Negative Binomial (NBp) Model
- Author
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Daniel A. Griffith
- Subjects
eigenvector spatial filter ,moment-generating function ,negative binomial ,population density ,Puerto Rico ,Mathematics ,QA1-939 - Abstract
This paper describes various selected properties and features of negative binomial (NB) random variables, with special reference to NB2 (i.e., p = 2), and some generalizations to NBp (i.e., p ≥ 2), specifications. It presents new results (e.g., the NBp moment-generating function) with regard to the relationship between a sample mean and its accompanying variance, as well as spatial statistical/econometric numerical and empirical examples, whose parameter estimators are maximum likelihood or method of moment ones. Finally, it highlights the Moran eigenvector spatial filtering methodology within the context of generalized linear modeling, demonstrating it in terms of spatial negative binomial regression. Its overall conclusion is a bolstering of important findings the literature already reports with a newly recognized empirical example of an NB3 phenomenon.
- Published
- 2024
- Full Text
- View/download PDF
4. Some Comments about the p-Generalized Negative Binomial (NBp) Model.
- Author
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Griffith, Daniel A.
- Subjects
RANDOM variables ,NEGATIVE binomial distribution ,MAXIMUM likelihood statistics ,NUMERICAL analysis ,ECONOMETRICS - Abstract
This paper describes various selected properties and features of negative binomial (NB) random variables, with special reference to NB2 (i.e., p = 2), and some generalizations to NBp (i.e., p ≥ 2), specifications. It presents new results (e.g., the NBp moment-generating function) with regard to the relationship between a sample mean and its accompanying variance, as well as spatial statistical/econometric numerical and empirical examples, whose parameter estimators are maximum likelihood or method of moment ones. Finally, it highlights the Moran eigenvector spatial filtering methodology within the context of generalized linear modeling, demonstrating it in terms of spatial negative binomial regression. Its overall conclusion is a bolstering of important findings the literature already reports with a newly recognized empirical example of an NB3 phenomenon. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
5. A precise mathematical approach for analyzing the performance of MIMO space–time block code systems over Weibull fading channels
- Author
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Abdelmajid Bessate, Youssef Miftah, Hussain Ben-Azza, and Faissal El Bouanani
- Subjects
Average symbol error rate ,Correlation ,Moment-generating function ,Multiple-input–multiple-output ,Monte Carlo simulation method ,Outage probability ,Telecommunication ,TK5101-6720 ,Electronics ,TK7800-8360 - Abstract
Abstract Multiple-input–multiple-output (MIMO) systems have effectively addressed today’s high demand for 5G communications and beyond. Further, MIMO-assisted space–time block codes (STBCs) have been shown to enhance the system’s performance and provide a complete variety of coherent flat-fading channels. Additionally, the closed-form expression of the probability density function of the summation of correlated Weibull random variables remains unknown. In this work, we investigate the performance analysis of MIMO-STBC-enabled systems subject to the Weibull fading channel. New tight approximate expressions for numerous system performance metrics, e.g., outage probability, average capacity under various rate adaption methods, and average symbol/bit error rate, have been obtained. The Monte Carlo simulation method has corroborated all the presented results.
- Published
- 2024
- Full Text
- View/download PDF
6. A precise mathematical approach for analyzing the performance of MIMO space–time block code systems over Weibull fading channels.
- Author
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Bessate, Abdelmajid, Miftah, Youssef, Ben-Azza, Hussain, and El Bouanani, Faissal
- Subjects
- *
SPACE-time block codes , *SYMBOL error rate , *MONTE Carlo method , *ERROR rates , *PROBABILITY density function , *RANDOM variables - Abstract
Multiple-input–multiple-output (MIMO) systems have effectively addressed today's high demand for 5G communications and beyond. Further, MIMO-assisted space–time block codes (STBCs) have been shown to enhance the system's performance and provide a complete variety of coherent flat-fading channels. Additionally, the closed-form expression of the probability density function of the summation of correlated Weibull random variables remains unknown. In this work, we investigate the performance analysis of MIMO-STBC-enabled systems subject to the Weibull fading channel. New tight approximate expressions for numerous system performance metrics, e.g., outage probability, average capacity under various rate adaption methods, and average symbol/bit error rate, have been obtained. The Monte Carlo simulation method has corroborated all the presented results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
7. Inference for Parameters of Exponential Distribution under Combined Type II Progressive Hybrid Censoring Scheme.
- Author
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Lee, Kyeongjun
- Subjects
- *
DISTRIBUTION (Probability theory) , *MAXIMUM likelihood statistics , *CENSORSHIP , *BAYESIAN field theory - Abstract
In recent years, various forms of progressive hybrid censoring schemes (PHCS) have gained significant traction in survival and reliability analysis studies due to their versatility. However, these PHCS variants are often characterized by complexity stemming from the multitude of parameters involved in their specification. Consequently, the primary objective of this paper is to propose a unified approach termed combined type II progressive hybrid censoring scheme ( ComT 2 PHCS) capable of encompassing several existing PHCS variations. Our analysis focuses specifically on the exponential distribution (ExDist). Bayesian inference techniques are employed to estimate the parameters of the ExDist under the ComT 2 PHCS. Additionally, we conduct fundamental distributional analyses and likelihood inference procedures. We derive the conditional moment-generating function (CondMGF) of maximum likelihood estimator (MLE) for parameters of the ExDist under ComT 2 PHCS. Further, we use CondMGF for the distribution of MLE for parameters of ExDist under ComT 2 PHCS. Finally, we provide an illustrative example to elucidate the inference methods derived in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
8. Closed-Form Formula for the Conditional Moment-Generating Function Under a Regime-Switching, Nonlinear Drift CEV Process, with Applications to Option Pricing
- Author
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Kittisak Chumpong, Khamron Mekchay, Fukiat Nualsri, and Phiraphat Sutthimat
- Subjects
nonlinear drift CEV process ,regime switching ,moment-generating function ,option pricing ,analytically pricing ,CIR process ,Mathematics ,QA1-939 - Abstract
An analytical derivation of the conditional moment-generating function (MGF) for a regime-switching nonlinear drift constant elasticity of variance process is established. The proposed model incorporates both regime-switching mechanisms and nonlinear drift components to better capture market phenomena such as volatility smiles and leverage effects. Regime-switching models can match the tendency of financial markets to often change their behavior abruptly and the phenomenon that the new behavior of financial variables often persists for several periods after such a change. Closed-form formulas for the MGF under various conditions, which are then applied for option pricing, are also derived. The efficacy and accuracy of the results are validated through a discrete Markov chain simulation. The results obtained from the proposed formulas completely match with those from MC simulations, while requiring significantly less computational time.
- Published
- 2024
- Full Text
- View/download PDF
9. A New Extension of the Exponentiated Weibull–Poisson Family Using the Gamma-Exponentiated Weibull Distribution: Development and Applications
- Author
-
Kuntalee Chaisee, Manad Khamkong, and Pawat Paksaranuwat
- Subjects
exponentiated Weibull distribution ,exponentiated Weibull–Poisson distribution ,gamma-exponentiated Weibull distribution ,maximum likelihood estimation ,moment-generating function ,Mathematics ,QA1-939 - Abstract
This study proposes a new five-parameter distribution called the gamma-exponentiated Weibull–Poisson (GEWP) distribution. As an extension of the exponentiated Weibull–Poisson family, the GEWP distribution offers a more flexible tool for analyzing a wider variety of data due to its theoretically and practically advantageous properties. It encompasses established distributions like the exponential, Weibull, and exponentiated Weibull. The development of the GEWP distribution proposed in this paper is obtained by combining the gamma–exponentiated Weibull (GEW) and the exponentiated Weibull–Poisson (EWP) distributions. Therefore, it serves as an extension of both the GEW and EWP distributions. This makes the GEWP a viable alternative for describing the variability of occurrences, enabling analysis in situations where GEW and EWP may be limited. This paper analyzes the probability distribution functions and provides the survival and hazard rate functions, the sub-models, the moments, the quantiles, and the maximum likelihood estimation of the GEWP distribution. Then, the numerical experiments for the parameter estimation of GEWP distribution for some finite sample sizes are presented. Finally, the comparative study of GEWP distribution and its sub-models is investigated via the goodness of fit test with real datasets to illustrate its potentiality.
- Published
- 2024
- Full Text
- View/download PDF
10. The Odd Beta Prime-G Family of Probability Distributions: Properties and Applications to Engineering and Environmental Data.
- Author
-
Suleiman, Ahmad Abubakar, Daud, Hanita, Othman, Mahmod, Ishaq, Aliyu Ismail, Indawati, Rachmah, Abdullah, Mohd Lazim, and Husin, Abdullah
- Subjects
PROBABILITY theory ,ENTROPY dimension ,GENERATING functions ,GENERALIZATION ,ENVIRONMENTAL databases ,ENGINEERING databases - Abstract
In this work, a novel generalized family of distributions called the odd beta prime is introduced. The linear representations of the proposed family are obtained. The expressions for the moments, the moment-generating function, and entropy are derived. A three-parameter special sub-model of the proposed family called the odd beta prime exponential distribution is proposed. Finally, two real data sets are used to illustrate the usefulness and flexibility of the proposed distribution. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
11. Inference for Parameters of Exponential Distribution under Combined Type II Progressive Hybrid Censoring Scheme
- Author
-
Kyeongjun Lee
- Subjects
Bayesian inference ,combined type II progressive hybrid censoring ,maximum likelihood estimator ,moment-generating function ,Mathematics ,QA1-939 - Abstract
In recent years, various forms of progressive hybrid censoring schemes (PHCS) have gained significant traction in survival and reliability analysis studies due to their versatility. However, these PHCS variants are often characterized by complexity stemming from the multitude of parameters involved in their specification. Consequently, the primary objective of this paper is to propose a unified approach termed combined type II progressive hybrid censoring scheme (ComT2PHCS) capable of encompassing several existing PHCS variations. Our analysis focuses specifically on the exponential distribution (ExDist). Bayesian inference techniques are employed to estimate the parameters of the ExDist under the ComT2PHCS. Additionally, we conduct fundamental distributional analyses and likelihood inference procedures. We derive the conditional moment-generating function (CondMGF) of maximum likelihood estimator (MLE) for parameters of the ExDist under ComT2PHCS. Further, we use CondMGF for the distribution of MLE for parameters of ExDist under ComT2PHCS. Finally, we provide an illustrative example to elucidate the inference methods derived in this paper.
- Published
- 2024
- Full Text
- View/download PDF
12. Some Families of Jensen-like Inequalities with Application to Information Theory.
- Author
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Merhav, Neri
- Subjects
- *
JENSEN'S inequality , *CONVEX functions , *RANDOM variables , *INFORMATION theory , *QUADRATIC equations - Abstract
It is well known that the traditional Jensen inequality is proved by lower bounding the given convex function, f (x) , by the tangential affine function that passes through the point (E { X } , f (E { X })) , where E { X } is the expectation of the random variable X. While this tangential affine function yields the tightest lower bound among all lower bounds induced by affine functions that are tangential to f, it turns out that when the function f is just part of a more complicated expression whose expectation is to be bounded, the tightest lower bound might belong to a tangential affine function that passes through a point different than (E { X } , f (E { X })) . In this paper, we take advantage of this observation by optimizing the point of tangency with regard to the specific given expression in a variety of cases and thereby derive several families of inequalities, henceforth referred to as "Jensen-like" inequalities, which are new to the best knowledge of the author. The degree of tightness and the potential usefulness of these inequalities is demonstrated in several application examples related to information theory. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
13. Global and Local Scaling Limits for Linear Eigenvalue Statistics of Jacobi β-Ensembles
- Author
-
Min, Chao, Chen, Yang, Gohberg, Israel, Founding Editor, Ball, Joseph A., Series Editor, Böttcher, Albrecht, Series Editor, Dym, Harry, Series Editor, Langer, Heinz, Series Editor, Tretter, Christiane, Series Editor, Basor, Estelle, editor, Ehrhardt, Torsten, editor, and Tracy, Craig A., editor
- Published
- 2022
- Full Text
- View/download PDF
14. Advanced Detection Techniques and Compensation of Channel Impairments
- Author
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Djordjevic, Ivan B. and Djordjevic, Ivan B.
- Published
- 2022
- Full Text
- View/download PDF
15. Sum of Dependent Variables Generated by Alternating Poisson Flow
- Author
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Andronov, Alexander, Mahareva, Kristina, Kacprzyk, Janusz, Series Editor, Gomide, Fernando, Advisory Editor, Kaynak, Okyay, Advisory Editor, Liu, Derong, Advisory Editor, Pedrycz, Witold, Advisory Editor, Polycarpou, Marios M., Advisory Editor, Rudas, Imre J., Advisory Editor, Wang, Jun, Advisory Editor, Kabashkin, Igor, editor, Yatskiv, Irina, editor, and Prentkovskis, Olegas, editor
- Published
- 2022
- Full Text
- View/download PDF
16. SOME PROBABILITY THEORY-BASED INEQUALITIES FOR THE INCOMPLETE GAMMA FUNCTION.
- Author
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FROM, STEVEN G.
- Subjects
- *
GAMMA functions , *ENGINEERING reliability theory - Abstract
In this paper, we present new inequalities and bounds involving the incomplete gamma function and related functions. Many of these new inequalities and bounds are based upon results, some well known and some not as well known, from probability theory and reliability theory. When these results are combined with other mathematical techniques, some very good upper and lower bounds are obtained. In particular, improvements of previously discussed bounds are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
17. Study on the smart grid vulnerability index based on the moment-generating function and distortion function.
- Author
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Zhang, Feng, Luo, Xiaoying, Li, Fengling, Li, Yun, Li, Yanbin, and Zhang, Pengyu
- Subjects
- *
SMART power grids , *ELECTRIC power distribution grids , *SUSTAINABLE development - Abstract
Although smart grids are characterized by self-healing, economy, high efficiency, and security, many hidden dangers exist in the development of smart grids due to a gradually expanding power grid and the continuous access of new energy to the power grid. Therefore, the development of smart grids, especially their reliability, security, and vulnerability, warrants further investigation. In this study, the vulnerability of smart grids is identified, and the vulnerability elements of smart grids are selected. Based on relevant theories, such as credibility and the combination of the credibility-based moment-generating function and the distortion function, a calculation model and framework of the vulnerability index of a smart grid are constructed. An empirical analysis is also conducted. This study provides a scientific basis for analyzing the vulnerability of smart grids and suggesting reasonable preventive measures and auxiliary decision-making information for relevant planning, design, and operation personnel, which contributes to the sustainable and healthy development of smart grids. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
18. A bimatrix variate gamma distribution
- Author
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Maryam Rafiei, Daya K. Nagar, Anis Iranmanesh, Saralees Nadarajah, and Shou Shih
- Subjects
Bimatrix gamma distribution ,Maximum likelihood ,Moment-generating function ,Zonal polynomial ,Mathematics ,QA1-939 - Abstract
In this article, a bimatrix gamma distributions is introduced. Various mathematical properties of the proposed distribution like marginal distributions, expected values, entropies, and moment generating function are derived. Also, distributions of sum, quotient, and product are investigated. Parameter estimation by the method of maximum likelihood is considered. A simulation study is performed to check the finite sample performance of the maximum likelihood estimators.
- Published
- 2022
- Full Text
- View/download PDF
19. Some Families of Jensen-like Inequalities with Application to Information Theory
- Author
-
Neri Merhav
- Subjects
Jensen’s inequality ,convex function ,concave function ,entropy ,capacity ,moment-generating function ,Science ,Astrophysics ,QB460-466 ,Physics ,QC1-999 - Abstract
It is well known that the traditional Jensen inequality is proved by lower bounding the given convex function, f(x), by the tangential affine function that passes through the point (E{X},f(E{X})), where E{X} is the expectation of the random variable X. While this tangential affine function yields the tightest lower bound among all lower bounds induced by affine functions that are tangential to f, it turns out that when the function f is just part of a more complicated expression whose expectation is to be bounded, the tightest lower bound might belong to a tangential affine function that passes through a point different than (E{X},f(E{X})). In this paper, we take advantage of this observation by optimizing the point of tangency with regard to the specific given expression in a variety of cases and thereby derive several families of inequalities, henceforth referred to as “Jensen-like” inequalities, which are new to the best knowledge of the author. The degree of tightness and the potential usefulness of these inequalities is demonstrated in several application examples related to information theory.
- Published
- 2023
- Full Text
- View/download PDF
20. The Odd Beta Prime-G Family of Probability Distributions: Properties and Applications to Engineering and Environmental Data
- Author
-
Ahmad Abubakar Suleiman, Hanita Daud, Mahmod Othman, Aliyu Ismail Ishaq, Rachmah Indawati, Mohd Lazim Abdullah, and Abdullah Husin
- Subjects
odd beta prime generalized family ,exponential distribution ,T-X transformer ,moments ,moment-generating function ,entropy ,Electronic computers. Computer science ,QA75.5-76.95 - Abstract
In this work, a novel generalized family of distributions called the odd beta prime is introduced. The linear representations of the proposed family are obtained. The expressions for the moments, the moment-generating function, and entropy are derived. A three-parameter special sub-model of the proposed family called the odd beta prime exponential distribution is proposed. Finally, two real data sets are used to illustrate the usefulness and flexibility of the proposed distribution.
- Published
- 2023
- Full Text
- View/download PDF
21. Convolutions for Bernoulli and Euler–Genocchi Polynomials of Order (r , m) and Their Probabilistic Interpretation †.
- Author
-
Frontczak, Robert and Tomovski, Živorad
- Subjects
- *
BERNOULLI polynomials , *BERNOULLI numbers , *EULER polynomials , *FUNCTIONAL equations , *DISTRIBUTION (Probability theory) , *POLYNOMIALS - Abstract
The main purpose of this article is to derive several convolutions for generalized Bernoulli and Euler–Genocchi polynomials of order (r , m) , B n (r , m) (x) and A n (r , m) (x) , respectively. These polynomials have been introduced recently and contain the generalized Bernoulli, Euler and Genocchi polynomials as special members. Some of our results extend the results of M. Merca and others concerning Bernoulli numbers and polynomials. Probabilistic interpretations of the presented results are also given. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
22. Molecular Weight Distribution Control for Polymerization Processes Based on the Moment-Generating Function.
- Author
-
Zhang, Jianhua, Pu, Jinzhu, and Ren, Mifeng
- Subjects
- *
MOLECULAR weights , *POLYMERIZATION , *SYSTEM identification , *EQUATIONS of state , *STYRENE - Abstract
The molecular weight distribution is an important factor that affects the properties of polymers. A control algorithm based on the moment-generating function was proposed to regulate the molecular weight distribution for polymerization processes in this work. The B-spline model was used to approximate the molecular weight distribution, and the weight state space equation of the system was identified by the subspace state space system identification method based on the paired date of B-spline weights and control inputs. Then, a new performance criterion mainly consisting of the moment-generating function was constructed to obtain the optimal control input. The effectiveness of the proposed control method was tested in a styrene polymerization process. The molecular weight distribution of the styrene polymers can be approximated by the B-spline model effectively, and it can also be regulated towards the desired one under the proposed control method. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
23. Union Bound on the Bit Error Rate for MIMO-GFDM Systems.
- Author
-
Wang, Yanpeng and Fortier, Paul
- Subjects
FREQUENCY division multiple access ,CHANNEL estimation ,NUMERICAL calculations ,ERROR probability ,BIT error rate ,MULTIPATH channels - Abstract
In this paper, a union bound on the bit error rate (BER) for multiple input multiple output generalized frequency division multiplexing (MIMO-GFDM) systems is derived based on exact pairwise error probabilities. The moment-generating function is used to calculate the exact pairwise error probability under the assumption that a maximum likelihood detector is used at the receiver. A realistic multipath MIMO channel environment is investigated in which the spatial correlation between antennas and the channel estimation errors are included. The Kronecker model and an additive model are used to describe the spatial correlation and channel estimation errors, respectively. The impacts of the spatial correlation and the channel estimation errors on the derived bound are investigated. The performances of MIMO-GFDM systems using different modulation techniques are also examined. Numerical calculations of the union bound and computer-based Monte-Carlo simulations of BER are carried out to verify the derived bound. Numerical results show that the derived union bound is a tight upper bound on the BER for MIMO-GFDM systems in a reasonable E s / N 0 region. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
24. Stochastic Volatility Option Pricing Models
- Author
-
Lee, Cheng-Few, Chen, Hong-Yi, Lee, John, Lee, Cheng-Few, Chen, Hong-Yi, and Lee, John
- Published
- 2019
- Full Text
- View/download PDF
25. Molecular Weight Distribution Control for Polymerization Processes Based on the Moment-Generating Function
- Author
-
Jianhua Zhang, Jinzhu Pu, and Mifeng Ren
- Subjects
molecular weight distribution ,moment-generating function ,B-spline ,Science ,Astrophysics ,QB460-466 ,Physics ,QC1-999 - Abstract
The molecular weight distribution is an important factor that affects the properties of polymers. A control algorithm based on the moment-generating function was proposed to regulate the molecular weight distribution for polymerization processes in this work. The B-spline model was used to approximate the molecular weight distribution, and the weight state space equation of the system was identified by the subspace state space system identification method based on the paired date of B-spline weights and control inputs. Then, a new performance criterion mainly consisting of the moment-generating function was constructed to obtain the optimal control input. The effectiveness of the proposed control method was tested in a styrene polymerization process. The molecular weight distribution of the styrene polymers can be approximated by the B-spline model effectively, and it can also be regulated towards the desired one under the proposed control method.
- Published
- 2022
- Full Text
- View/download PDF
26. On the Distribution of the Sum of Málaga-M Random Variables and Applications.
- Author
-
Illi, Elmehdi, Bouanani, Faissal El, and Ayoub, Fouad
- Subjects
- *
SYMBOL error rate , *PROBABILITY density function , *RANDOM variables , *RECEIVER operating characteristic curves , *FREE-space optical technology - Abstract
In this paper, a very accurate approximation method for the statistics of the sum of Málaga-M random variates with pointing error (MRVs) is proposed. In particular, the probability density function of MRV is approximated by a Fox's H-function through the moment-based approach. Then, the respective moment-generating function of the sum of N MRVs is provided, based on which the average symbol error rate is evaluated for an N-branch maximal-ratio combining (MRC) receiver. The retrieved results show that the proposed approximate results match accurately with the exact simulated ones. Additionally, the results show that the achievable diversity order increases as a function of the number of MRC diversity branches. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
27. Differential Faster-Than-Nyquist Signaling
- Author
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Takumi Ishihara and Shinya Sugiura
- Subjects
Analytical bound ,differential modulation ,faster-than-Nyquist ,frequency-domain equalization ,inter-symbol interference ,moment-generating function ,Electrical engineering. Electronics. Nuclear engineering ,TK1-9971 - Abstract
In this paper, we propose a novel differential faster-than-Nyquist (DFTN) signaling concept that allows us to dispense with any channel estimation at the receiver, while benefiting from a rate boost specific to faster-than-Nyquist (FTN) signaling. More specifically, at the transmitter, differentially modulated phaseshift keying (DPSK) symbols are transmitted with a symbol interval that is smaller than that defined by the Nyquist criterion. The receiver first equalizes the DPSK symbols, which suffer from the effects of FTN-specific inter-symbol interference (ISI), with the aid of frequency-domain equalization (FDE). Then, the equalized symbols are differentially demodulated in a noncoherent manner. This noncoherent detection is enabled, by relying on the fact that FTN-specific ISI is deterministic when the FTN's symbol packing ratio and the roll-off factor of a shaping filter are known in advance of transmissions. Moreover, we derive an analytical bound on the achievable bit error ratio for the proposed DFTN signaling, based on moment-generating functions. This is achieved by introducing an equivalent signal-to-interference-and-noise ratio for the DPSK symbols after FDE. Our simulation results demonstrate that our DFTN receiver is capable of noncoherently demodulating the DFTN symbols when the symbol packing ratio is not substantially low.
- Published
- 2018
- Full Text
- View/download PDF
28. Moments of the quadrivariate Rayleigh distribution with applications for diversity receivers.
- Author
-
Tekinay, Mustafa and Beard, Cory
- Abstract
Wireless channels exhibit time, frequency, and spatial correlation. Models in literature that study four-branch diversity receivers make assumptions such as independence, constant correlation, exponential correlation, or some other kind between received signals at each antenna. However, these models are not accurate in many scenarios. Addressing this issue, we provide novel results for the moments, moment-generating function, probability density function, and cumulative distribution function of the quadrivariate Rayleigh distribution with an arbitrary correlation model. To the best of our knowledge, our model is the most comprehensive and the only one that can incorporate the 3GPP suggested spatial correlation structure. We use our new results to derive an analytical expression for the moments of the output signal-to-noise ratio of the four-branch equal gain combining receiver and the four-branch maximal ratio combining receiver. We provide original insight about their output signal-to-noise ratio distributions through their higher order moments in different scenarios. Our expressions are valid for all moments. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
29. Effective capacity and outage analysis using moment-generating function over Nakagami-m and Rayleigh fading channels in cooperative communication system.
- Author
-
Zahedi, Abdulhamid
- Abstract
Cooperative communication using multiple relays improves quality of service (QoS) parameters of a communication system. To verify this improvement, accurate analysis must be done considering the various fading channels and probability density function (PDF) or cumulative distribution function (CDF) of signal-to-noise ratio (SNR) in relays and destination. In this paper, using the moment-generating function (MGF) method and considering Nakagami-m fading channel, the outage probability and effective capacity are analyzed. Obtaining the closed-form expression of outage probability and effective capacity in Nakagami-m fading channel includes complex mathematical calculations; thus, the Rayleigh fading channel is assumed to be a special case of Nakagami-m distribution to achieve simpler mathematical equations. Simulation results verify the mathematical analysis in terms of effective capacity and outage probability. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
30. On the Relationships Between Average Channel Capacity, Average Bit Error Rate, Outage Probability, and Outage Capacity Over Additive White Gaussian Noise Channels.
- Author
-
Yilmaz, Ferkan
- Subjects
- *
ERROR probability , *ADDITIVE white Gaussian noise channels , *ERROR rates , *NOISE , *PROBABILITY theory , *TELECOMMUNICATION systems - Abstract
In the theory of wireless communications, average performance measures (APMs) are widely utilized to quantify the performance gains/impairments in various fading environments under various scenarios, and to comprehend how the factors arising from design/implementation affect system performance. To the best of our knowledge, it has not been yet discovered in the literature how these APMs relate to each other. In this article, to supplement the APM analyses available in the literature we propose that one APM can be calculated using the other APMs instead of using the end-to-end SNR distribution. Particularly, using the Lamperti’s transformation (LT), we propose a tractable approach, which we call LT-based APM analysis, to identify a relationship between any two given APMs such that it is irrespective of SNR distribution. Thereby, we introduce some novel relationships among average channel capacity (ACC), average bit error rate (ABER) and outage probability/capacity (OP/OC) performances, and accordingly present how to obtain ACC from ABER performance and how to obtain OP/OC from ACC performance in fading environments. We demonstrate that the ACC of any communications system can be evaluated empirically without using end-to-end SNR distribution. We consider some numerical examples and simulations to validate our newly derived relationships. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
31. Mean-Reverting 4/2 Principal Components Model. Financial Applications
- Author
-
Marcos Escobar-Anel and Zhenxian Gong
- Subjects
principal component analysis ,4/2 stochastic volatility model ,moment-generating function ,risk management calculations ,Insurance ,HG8011-9999 - Abstract
In this paper, we propose a new multivariate mean-reverting model incorporating state-of-the art 4/2 stochastic volatility and a convenient principal component stochastic volatility (PCSV) decomposition for the stochastic covariance. We find a quasi closed-form characteristic function and propose analytic approximations, which aid in the pricing of derivatives and calculation of risk measures. Parameters are estimated on three bivariate series, using a two-stage methodology involving method of moments and least squares. Moreover, a scaling factor is added for extra degrees of freedom to match data features. As an application, we consider investment strategies for a portfolio with two risky assets and a risk-free cash account. We calculate value-at-risk (VaR) values at a 95% risk level using both simulation-based and distribution-based methods. A comparison of these VaR values supports the effectiveness of our approximations and the potential for higher dimensions.
- Published
- 2021
- Full Text
- View/download PDF
32. Performance Analysis of a UAV-Assisted RF/FSO Relaying Systems for Internet of Vehicles
- Author
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Guanjun Xu and Zhaohui Song
- Subjects
Computer Networks and Communications ,Computer science ,business.industry ,Cumulative distribution function ,Probability density function ,Function (mathematics) ,Moment-generating function ,Communications system ,Computer Science Applications ,Hardware and Architecture ,Signal Processing ,Electronic engineering ,Fading ,The Internet ,Radio frequency ,business ,Information Systems - Abstract
The Internet of Vehicles (IoV), as a development and complement of the Internet of Thing, has attracted extensive attention and is expected to play a crucial role in human society with the matured Space-Air-Ground Integrated Networks (SAGIN). Here, we devote ourselves to establish and investigate a UAV-assisted radio frequency (RF)/free space optical (FSO) communication system under the amplified-and-forward protocol with variable gain. More specifically, we assume the RF link follows κ-μ fading and the FSO link experiences Malaga fading, which can characterize the atmospheric turbulence under weak-to-strong condition excellently. In addition, both the pointing errors impairment and the detection techniques for the FSO link are also taken into account. Novel analytical expressions for the end-to-end system, e.g., the cumulative distribution function, probability density function, and moment generating function, are proposed. By capitalizing on these results, some system metrics of the UAV-assisted relaying system are given with the Meijer’s G function. To providing more insights for this UAV-assisted system for SAGIN, high signal-to-noise approximations of these metrics are also presented. Furthermore, the approximated expressions for the outage probability and average BER are given in presence of non-pointing error effect. Finally, all these analytical results are validated with the Monte-Carlo simulations.
- Published
- 2022
33. Appendix: Probability and Mathematical Concepts
- Author
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Rohde, Charles A. and Rohde, Charles A.
- Published
- 2014
- Full Text
- View/download PDF
34. A New Method for Model-Based Health Economic Evaluation Utilizing and Extending Moment-Generating Functions.
- Author
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Snowsill, Tristan
- Abstract
Background. Health economic evaluations frequently include projections for lifetime costs and health effects using modeling frameworks such as Markov modeling or discrete event simulation (DES). Markov models typically cannot represent events whose risk is determined by the length of time spent in state (sojourn time) without the use of tunnel states. DES is very flexible but introduces Monte Carlo variation, which can significantly limit the complexity of model analyses. Methods. We present a new methodological framework for health economic modeling that is based on, and extends, the concept of moment-generating functions (MGFs) for time-to-event random variables. When future costs and health effects are discounted, MGFs can be used to very efficiently calculate the total discounted life-years spent in a series of health states. Competing risks are incorporated into the method. This method can also be used to calculate discounted costs and health effects when these payoffs are constant per unit time, one-off, or exponential with regard to time. MGFs are extended to additionally support costs and health effects which are polynomial with regard to time (as in a commonly used model of population norms for EQ-5D utility). Worked Example. A worked example is used to demonstrate the application of the new method in practice and to compare it with Markov modeling and DES. Results are compared in terms of convergence and accuracy, and computation times are compared. R code and an Excel workbook are provided. Conclusions. The MGF method can be applied to health economic evaluations in the place of Markov modeling or DES and has certain advantages over both. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
35. CROSS-MOMENTS COMPUTATION FOR STOCHASTIC CONTEXT-FREE GRAMMARS.
- Author
-
Ilić, Velimir M., Ćirić, Miroslav D., and Stanković, Miomir S.
- Subjects
- *
GRAMMAR , *PARTITION functions - Abstract
In this paper we consider the problem of efficient computation of cross-moments of a vector random variable represented by a stochastic context-free grammar. Two types of cross-moments are discussed. The sample space for the first one is the set of all derivations of the context-free grammar, and the sample space for the second one is the set of all derivations which generate a string belonging to the language of the grammar. In the past, this problem was widely studied, but mainly for the cross-moments of scalar variables and up to the second order. This paper presents new algorithms for computing the cross-moments of an arbitrary order, while the previously developed ones are derived as special cases. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
36. Pseudo-exponential distribution and its statistical applications in econophysics.
- Author
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Mehri-Dehnavi, Hossein, Agahi, Hamzeh, and Mesiar, Radko
- Subjects
- *
BOLTZMANN machine , *BOLTZMANN'S equation , *FUZZY systems , *APPLIED mathematics , *PARTIAL differential equations - Abstract
In generalized measure theory, σ-⊕-measure is a generalization of the classical measure defined on a pseudo-addition. In this paper, the class of pseudo-exponential distributions based on a class of σ-⊕-measure is introduced. Some examples of this class are investigated. Then by two real data sets obtained from the last three decades of oil, and the last two decades of the daily natural gas spot prices, we show that the pseudo-exponential distribution is better fitted than exponential distribution using the AIC and BIC information criteria. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
37. Dual-Hop RF/FSO Systems Over $\kappa$-$\mu$ Shadowed and Fisher-Snedecor ${\mathcal F}$ Fading Channels With Non-Zero Boresight Pointing Errors
- Author
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Dongpeng Kang, Jing Ma, Xiaolong Xie, Junrong Ding, and Liying Tan
- Subjects
Physics ,Cumulative distribution function ,Monte Carlo method ,Bit error rate ,Gamma distribution ,Elementary function ,Probability density function ,Fading ,Statistical physics ,Moment-generating function ,Atomic and Molecular Physics, and Optics - Abstract
We investigate the performance of a dual-hop mixed radio frequency (RF)/free space optical (FSO) system with variable-gain relaying. The RF link is modeled by the κ-μ shadowed distribution, which unifies popular RF channel models. The FSO link is subject to atmospheric turbulence with non-zero boresight pointing errors. The atmospheric turbulence channel is modeled by the Fisher-Snedecor 𝓕 distribution, which fits well with the measurement data under weak-to-strong turbulence conditions. The pointing error is modeled by the Beckmann distribution, which includes popular pointing error models. We propose an approximation method to approximate the κ-μ shadowed distribution using an α-μ distribution, which is more accurate than that using a gamma distribution in the existing literatures. Then, we derive closed-form expressions for the probability density function (PDF) and the cumulative distribution function (CDF) for the irradiance fluctuations. Based on these expressions, we derive closed-form approximate expressions for the CDF, the PDF, the moment generating function (MGF), the average bit error rate (BER), and the ergodic capacity (EC) of the considered system in terms of the bivariate Fox's H function. Furthermore, asymptotic expressions for the CDF and the average BER at high signal-to-noise ratio (SNR) are derived in terms of simple elementary functions. Finally, numerical results and Monte Carlo (MC) simulations are provided to verify the derived approximate expressions.
- Published
- 2022
38. A new family of multivariate skew slash distribution.
- Author
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Tian, Weizhong, Wang, Tonghui, and Gupta, Arjun K.
- Subjects
- *
MULTIVARIATE analysis , *SKEWNESS (Probability theory) , *QUADRATIC forms , *RANDOM variables , *PROBABILITY theory - Abstract
In this article, the new family of multivariate skew slash distribution is defined. According to the definition, a stochastic representation of the multivariate skew slash distribution is derived. The first four moments and measures of skewness and kurtosis of a random vector with the multivariate skew slash distribution are obtained. The distribution of quadratic forms for the multivariate skew slash distribution and the non central skew slash χ2 distribution are studied. Maximum likelihood inference and real data illustration are discussed. In the end, the potential extension of multivariate skew slash distribution is discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
39. Univariate and Bivariate Alpha-Power Transformed Lomax Distribution: Properties and Application
- Author
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Rania Shalabi, Dina H. Abdelhady, and Yasser Anmer
- Subjects
education.field_of_study ,Joint probability distribution ,Population ,Univariate ,Estimator ,Applied mathematics ,Lomax distribution ,Bivariate analysis ,Moment-generating function ,education ,Mathematics ,Copula (probability theory) - Abstract
A new method for adding parameters to a well-established distribution to obtain more flexible new families of distributions is applied to Lomax distribution (LD). This method is known as the Alpha-Power transformation (APT) and introduced by Mahdavi and Kundu (2015). The reliability and statistical properties of the proposed models are studied. Maximum likelihood method of estimation is utilized to obtain the estimators of the population parameters. The extended model is applied on a real data and the results are given and compared to other models. Also, a bivariate distribution was constructed from the proposed distribution using the Farlie-Gumbel-Morgenstern (FGM) copula. Some characteristics of this distribution and the estimation using the maximum likelihood are shown on a real data.
- Published
- 2022
40. A New Neutrosophic Negative Binomial Distribution: Properties and Applications
- Author
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Rehan Ahmad Khan Sherwani, Sadia Sagar Iqbal, Ali Hussein Al-Marshadi, Muhammad Aslam, and Shumaila Abbas
- Subjects
Article Subject ,Distribution (number theory) ,Characteristic function (probability theory) ,General Mathematics ,media_common.quotation_subject ,Order statistic ,Negative binomial distribution ,Ambiguity ,Moment-generating function ,Inverse Mills ratio ,QA1-939 ,Applied mathematics ,Probability distribution ,Mathematics ,media_common - Abstract
Many problems in real life exist that are full of confusion, vagueness, and ambiguity. The quantification of such issues in a scientific way is the need of time. The negative binomial distribution is an important discrete probability distribution from the account of classical probability distribution theory. The distribution was used to study the chance of kth success in n trials before n − 1 failures for crisp data. The literature lacks in dealing with the situations for interval-valued data under negative binomial distribution. In this research, the neutrosophic negative binomial distribution is proposed to generalize the classical negative binomial distribution. The generalized proposed distribution considers the indeterminacy and crisp form from interval-valued. Several properties of the proposed distribution, such as moment generating function, characteristic function, and probability generating function, are also derived. Furthermore, the derivation of reliability analysis properties such as survival, hazard rate, reversed hazard rate, cumulative hazard rate, mills ratio, and odds ratio are also presented. In addition, order statistics for the proposed distribution, including w th , joint, median, minimum, and maximum order statistics are part of the paper. The proposed distribution is discussed from the real data applications perspective by considering the different case studies. This research opens the way to deal with the problems that follow conventional conveyances and include nonprecisely determined details simultaneously.
- Published
- 2021
41. Average Achievable Rate and Average BLER Analyses for MIMO Short-Packet Communication Systems
- Author
-
Jianchao Zheng, Qi Zhang, and Jiayin Qin
- Subjects
Wishart distribution ,Computer Networks and Communications ,ComputerSystemsOrganization_COMPUTER-COMMUNICATIONNETWORKS ,MIMO ,Aerospace Engineering ,Inverse Laplace transform ,Data_CODINGANDINFORMATIONTHEORY ,Moment-generating function ,Communications system ,Upper and lower bounds ,Block Error Rate ,Automotive Engineering ,Electrical and Electronic Engineering ,Algorithm ,Computer Science::Information Theory ,Mathematics ,Rayleigh fading - Abstract
Multiple-input-multiple-output (MIMO) systems significantly increase the network throughput and coverage probability for short-packet communications. In this paper, a tight lower bound on the average achievable rate of MIMO short-packet communication systems is theoretically derived, considering flat uncorrelated Rayleigh fading MIMO channels. The derivations are based on the eigenvalue analysis of a Wishart matrix and Jensen's inequality. Given the actual transmission rate, a tight approximation on the average block error rate (BLER) of MIMO short-packet communication systems is also provided, which is based on the moment generating function and inverse Laplace transform. Numerical results demonstrate that both our theoretically derived analytical average achievable rate lower bound and approximate average BLER are almost the same as the simulation results.
- Published
- 2021
42. Sine Half-Logistic Inverse Rayleigh Distribution: Properties, Estimation, and Applications in Biomedical Data
- Author
-
Mohammed Elgarhy, M. Shrahili, and Ibrahim Elbatal
- Subjects
Article Subject ,Rayleigh distribution ,General Mathematics ,Tsallis entropy ,Mathematical analysis ,Inverse ,Moment-generating function ,Quantile function ,Physics::Fluid Dynamics ,Moment (mathematics) ,Rényi entropy ,symbols.namesake ,QA1-939 ,symbols ,Rayleigh scattering ,Mathematics ,Computer Science::Information Theory - Abstract
A new lifetime distribution with two parameters, known as the sine half-logistic inverse Rayleigh distribution, is proposed and studied as an extension of the half-logistic inverse Rayleigh model. The sine half-logistic inverse Rayleigh model is a new inverse Rayleigh distribution extension. In the application section, we show that the sine half-logistic inverse Rayleigh distribution is more flexible than the half-logistic inverse Rayleigh and inverse Rayleigh distributions. The statistical properties of the half-logistic inverse Rayleigh model are calculated, including the quantile function, moments, moment generating function, incomplete moment, and Lorenz and Bonferroni curves. Entropy measures such as Rényi entropy, Havrda and Charvat entropy, Arimoto entropy, and Tsallis entropy are proposed for the sine half-logistic inverse Rayleigh distribution. To estimate the sine half-logistic inverse Rayleigh distribution parameters, statistical inference using the maximum likelihood method is used. Applications of the sine half-logistic inverse Rayleigh model to real datasets demonstrate the flexibility of the sine half-logistic inverse Rayleigh distribution by comparing it to well-known models such as half-logistic inverse Rayleigh, type II Topp–Leone inverse Rayleigh, transmuted inverse Rayleigh, and inverse Rayleigh distributions.
- Published
- 2021
43. The Alpha Power Transformed Dagum Distribution: Properties and Applications
- Author
-
G. G. Hamedani, Hesham Reyad, Soha Othman, and Farrukh Jamal
- Subjects
Rényi entropy ,Dagum distribution ,Observed information ,Order statistic ,Monte Carlo method ,Statistical physics ,Moment-generating function ,Quantile function ,Stochastic ordering ,Mathematics - Abstract
In this study, we propose a new extension of the Dagum distribution called the alpha power transformed Dagum distribution. Basic statistical properties of the new distribution such as; quantile function, raw and incomplete moments, moment generating function, order statistics, Rényi entropy, stochastic ordering and stress strength model are investigated. The characterizations of the new model is investigated. The method of maximum likelihood is used to estimate the model parameters of the new distribution and the observed information matrix is also obtained. A Monte Carlo simulation is presented to examine the behavior of the parameter estimates. The applicability of the new model is demonstrated by means of three applications.
- Published
- 2021
44. Some Properties and Applications of Topp Leone Kumaraswamy Lomax Distribution
- Author
-
Sule Ibrahim, M. Jibril Haruna, Sani I. Doguwa, and Audu Isah
- Subjects
Hazard (logic) ,Distribution (mathematics) ,Plane (geometry) ,Maximum likelihood ,Statistics ,Lomax distribution ,Moment-generating function ,Quantile function ,Odds ,Mathematics - Abstract
Many Statisticians have developed and proposed new distributions by extending the existing distributions. The distributions are extended by adding one or more parameters to the baseline distributions to make it more flexible in fitting different kinds of data. In this study, a new four-parameter lifetime distribution called the Topp Leone Kumaraswamy Lomax distribution was introduced by using a family of distributions which has been proposed in the literature. Some mathematical properties of the distribution such as the moments, moment generating function, quantile function, survival, hazard, reversed hazard and odds functions were presented. The estimation of the parameters by maximum likelihood method was discussed. Three real life data sets representing the failure times of the air conditioning system of an air plane, the remission times (in months) of a random sample of one hundred and twenty-eight (128) bladder cancer patients and Alumina (Al2O3) data were used to show the fit and flexibility of the new distribution over some lifetime distributions in literature. The results showed that the new distribution fits better in the three datasets considered.
- Published
- 2021
45. Average of product of two Gaussian Q functions as summation series and its significance in evaluating SEP integrals over fading channels
- Author
-
Supriya Aggarwal
- Subjects
Series (mathematics) ,Computer Networks and Communications ,Applied Mathematics ,Gaussian ,Moment-generating function ,Range (mathematics) ,symbols.namesake ,Exponential sum ,Control and Systems Engineering ,Product (mathematics) ,Signal Processing ,Modulation (music) ,symbols ,Applied mathematics ,Fading ,Mathematics - Abstract
The product of two Gaussian Q -functions is actively used in computing the error probabilities of various digital modulation schemes. Evaluating symbol error probability (SEP) integral involving the product of Gaussian Q -functions over fading distributions is complicated. The closed-form solutions are not available always, therefore to derive these solutions approximations are used. In this paper, an approximation to the product of two Gaussian- Q functions as a sum of exponentials is presented. Further it is used to evaluate the error probabilities of modulation techniques over fading distributions in wide range of scenarios. The knowledge of moment generating function (MGF) of a fading model is sufficient enough to derive the closed-form solution to SEP integrals. Numerical results demonstrate superior accuracy of proposed approximation over other existing competing approximations. Furthermore the proposed solutions are fairly simple as the MGF of fading channels involve fundamental mathematical functions.
- Published
- 2021
46. Some Useful Integral Representations for Information-Theoretic Analyses
- Author
-
Neri Merhav and Igal Sason
- Subjects
integral representation ,logarithmic expectation ,moment-generating function ,fractional moments ,Rényi entropy ,jamming ,Science ,Astrophysics ,QB460-466 ,Physics ,QC1-999 - Abstract
This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas for quantities that involve expectations of the logarithm of a positive random variable. Here, in the same spirit, we derive an exact integral representation (in one or two dimensions) of the moment of a nonnegative random variable, or the sum of such independent random variables, where the moment order is a general positive non-integer real (also known as fractional moments). The proposed formula is applied to a variety of examples with an information-theoretic motivation, and it is shown how it facilitates their numerical evaluations. In particular, when applied to the calculation of a moment of the sum of a large number, n, of nonnegative random variables, it is clear that integration over one or two dimensions, as suggested by our proposed integral representation, is significantly easier than the alternative of integrating over n dimensions, as needed in the direct calculation of the desired moment.
- Published
- 2020
- Full Text
- View/download PDF
47. The Proof of Theorems 8.3, 8.5 and Example 8.7
- Author
-
Major, Péter and Major, Péter
- Published
- 2013
- Full Text
- View/download PDF
48. On the Distribution of a Quadratic Form in Normal Variates
- Author
-
Jin Zhang
- Subjects
eigenvalues ,idempotent matrices ,moment-generating function ,normality ,Statistics ,HA1-4737 ,Probabilities. Mathematical statistics ,QA273-280 - Abstract
It is a well-known theorem in linear models that the idempotency of a matrix is a sufficient and necessary condition for a quadratic form in normal variates to have a chisquare distribution, but its proofs in the early literature were incorrect or incomplete. Driscoll (1999) provided an improved proof, and this article presents a simple proof. More importantly, we establish and prove a generalized theorem.
- Published
- 2018
- Full Text
- View/download PDF
49. The distribution of the sum of independent and non identically generalized Lindley random variables
- Author
-
Hidetoshi Murakami, Masato Kitani, and Hiroki Hashiguchi
- Subjects
Statistics and Probability ,Variables ,Confluent hypergeometric function ,Distribution (number theory) ,Stochastic modelling ,media_common.quotation_subject ,Moment-generating function ,Lindley distribution ,Statistics::Methodology ,Order (group theory) ,Applied mathematics ,Random variable ,Mathematics ,media_common - Abstract
The original or generalized Lindley distribution has been proposed in order to fit a stochastic model to real data, that is, it establishes the distribution of the sum of independent variables. The...
- Published
- 2021
50. Exponentiated Power Muth Distribution and Associated Inference
- Author
-
Anuresha Krishna, R. Maya, and M. R. Irshad
- Subjects
Hazard (logic) ,Distribution (number theory) ,Bathtub ,Inference ,Applied mathematics ,Function (mathematics) ,Moment-generating function ,Measure (mathematics) ,Expression (mathematics) ,Mathematics - Abstract
In this article we introduce a generalized form of power Muth distribution, so-called exponentiated power Muth distribution with increasing, decreasing, bathtub and upside-down bathtub shaped hazard rates and investigate its important properties including analytical expression for moments based on generalized integro-exponential function, moment generating function, reliability measures and an uncertainty measure extropy. The maximum likelihood estimation method is used to estimate the parameters of the model and their performance is assessed via simulation study. Finally, the supremacy of the model is illustrated compared to its sub models and some other competing models using eight real data sets from diverse fields.
- Published
- 2021
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