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In this paper, we introduce a general class of lifetime distributions, called the two-sided Topp-Leone generated family of distribution. A special case of new family is the two-sided Topp-Leone Weibull distribution. This distribution used the two-sided Topp-Leone distribution as a generator for the Weibull distribution. The two-sided Topp-Leone Weibull distribution is presented in several shapes of distributions such as decreasing, unimodal, and bimodal which make this distribution more than flexible than the Weibull distribution. Its quantile function is presented. The parameter estimation method by using maximum likelihood estimation is discussed. The proposed distribution is applied to the strength data set, remission times of bladder cancer patients data set and time to failure of turbocharger data set. We compare the proposed distribution to the Topp-Leone Generated Weibull distribution. In conclusion, the two-sided Topp-Leone Weibull distribution performs similarly as the Topp-Leone Generated Weibul...

Continuous mixture Weibull models arise in many areas of sciences such as reliability studies, communications theory, etc. Due to its wide applicability, we introduce a class of continuous mixture Weibull models which is a combination of Weibull and generalized gamma distributions. Some characteristics of the distribution are obtained. It is seen that Kratzel integral enters into the model naturally, and then the model can be called as a Kratzel density. Applications of the density function related to fading channels and ultrasonic backscatter signals modeling are discussed. A real data analysis is given to illustrate the use of this distribution.

We discuss here the design of constant-stress accelerated life-tests for one-shot device testing by assuming a Weibull distribution as a lifetime model. Because there are no explicit expressions for the maximum likelihood estimators of the model parameters and their variances, we adopt the asymptotic approach here to develop an algorithm for the determination of optimal allocation of devices, inspection frequency, and the number of inspections at each stress level, by assuming a Weibull distribution with non-constant scale and shape parameters as the lifetime distribution. The asymptotic variance of the estimate of reliability of the device at a specified mission time is minimized subject to a pre-fixed experimental budget, and a termination time. Examples are provided to illustrate the proposed algorithm for the determination of the best test plan. A sensitivity analysis of the best test plan is also carried out to examine the effect of misspecification of the model parameters.

In this paper, we model block error rate (BLER) performance of optical wireless communication systems in strong turbulence slant channels with very slow fading and additive Gaussian noise, using the Exponentiated Weibull distribution models. In a communication system, which transmits data in blocks of N bits, the BLER probability P ( M , N ) of more than M bit errors in a block is particularly useful in evaluating the wireless optical channel performance. The joint effects of the beam wander and spread, pointing errors and the spectral index of non-Kolmogorov turbulence on system's performance are included. The obtained results can be essential for the designing of such links under real circumstances.

When the device is inspected only once, there are only two possible statuses either functioning or failed at the time of inspection. In this paper, we consider a series system consisting of two components with lifetimes following weibull distributions and a competing risks model is used to study the series system for quantal-response data. Based on the quantal-response data, the maximum likelihood estimates of parameters of weibull distribution are derived. The model is illustrated using a practical numerical example of two-component series products, and the statistical properties of the maximum likelihood estimators were studied via Monte Carlo simulation under three-stage inspected scheme for various sampling sizes. This study verified that the model is practical. This research results can be applied to the reliability analysis of one-shot products with Weibull components lifetime distribution and the stockpile storage performance test.

In order to make statistic analysis on lifetime data for web game, the two-parameter Weibull distribution was applied to describe its distribution. The shape parameter and the scale parameter were given by maximum likelihood estimation. When a web game followed Weibull distribution, the lifetime parameters are calculated via Matlab. The results show that the proposed model is appropriate to estimate the web game lifetime.

We derive explicit expressions for the moments, incomplete moments, quantile function and generating function of the additive Weibull model pioneered by Xie and Lai (1995), which is a quite flexible distribution for fitting lifetime data with bathtub-shaped failure rate function. In addition, we estimate the model parameters by maximum likelihood and determine the observed information matrix. The flexibility of the additive Weibull distribution is illustrated by means of one application to real data.

Modern satellite communication networks will employ frequencies above 10GHz. At these frequency bands, rain attenuation is the dominant fading mechanism. In this paper, a novel channel model, a synthesizer for generating rain attenuation time series for satellite links operating at 10GHz and above is presented. The proposed channel model modifies Maseng-Bakken (M-B) model since it generates rain attenuation time series that follow the Weibull distribution. The new stochastic dynamic model is based on the first-order Stochastic Differential Equations (SDEs) and considers rain attenuation induced on a slant path as a Weibull-based stochastic process. Moreover, the theoretical expressions for the computation of the exceedance probability of hitting time random variable are presented. The hitting time statistics may be employed for the optimum design of Fade Mitigation Techniques (FMTs). The synthesizer is verified in terms of the exceedance probability and the theoretical CCDF of hitting time comparing to these derived from the simulations in the numerical results section.

It is well known that the Weibull distribution is the most popular and the most widely used distribution in reliability and in analysis of lifetime data. Unfortunately, its hazard function cannot exhibit non-monotonic shapes like the bathtub shape or the unimodal shape. Since 1958, the Weibull distribution has been modified by many researchers to allow for non-monotonic hazard functions. This paper gives an extensive review of some discrete and continuous versions of the modifications of the Weibull distribution.

In this paper, we consider a dual hop wireless communication system with a non-regenerative relay and study its performance over the α-µ fading channel. Specifically, we derive closed-form expressions for the moment generating function (MGF), the cumulative distribution function (CDF), and the probability density function (PDF) of the harmonic mean of the end-to-end signal-to-noise ratio (SNR) assuming the α-µ fading model. We also derive closed-form expressions for the end-to-end capacity and outage capacity of the system herein. The obtained expressions can be reduced to study the performance of dual hop communication systems over other fading channel models by using the proper values for the α and µ parameters, such as Rayleigh, Nakagami-m, and Weibull fading models. Numerical results are provided for the obtained expressions and conclusion remarks are drawn.

In this paper, a closed-form expression for the moment generating function (MGF) of the instantaneous signal to noise ratio (SNR) per symbol is derived for Weibull fading channels. The derived MGF is valid for the rational values of fading parameter and it is shown to be useful for analyzing the symbol error rate for the case of M-ary phase shift keying and M-ary quadrature amplitude modulation schemes. Also, the outage probability can be accurately evaluated by using the probability density function of instantaneous SNR considered in this work.

In recent years, the Weibull distribution has been commonly used and recommended to model the wind speed. Therefore, many estimators have been proposed to find the best method to estimate the parameters of the Weibull distribution. Particularly, the estimator based on regression procedures with the Weibull probability plot are often used because of its computational simplicity and graphical presentation. However, when the procedure is applied, in many cases heteroscedasticity or non-normality of the error terms may be encountered. One way to handle this problem is using transformation techniques. In this study, the regression estimation based on data transformation is considered to estimate the parameters of the Weibull distribution. The simulation results show that the considered estimator based on the data transformation for the shape parameter of the Weibull distribution provides better performance than least squares estimator in terms of bias and mean square errors for the most of the considered cases.

Proposed by the Swedish engineer and mathematician Ernst Hjalmar Waloddi Weibull (1887-1979), the Weibull distribution is a probability distribution that is widely used to model lifetime data. Because of its flexibility, some modifications of the Weibull distribution have been made from several researches in order to best adjust the non-monotonic shapes. This paper gives a study on the performance of two specific modifications of the Weibull distribution which are the exponentiated Weibull distribution and the additive Weibull distribution.

We propose a simple analytical method for evaluating the average bit-error rate (BER) performance of multiple input multiple output (MIMO) free-space optical (FSO) communication systems over independent exponentiated Weibull (EW) channels. We first present an accurate approximation to the probability density function (PDF) of the sum of independent EW random variables corresponding to the EW-distributed FSO channel fading. Then, a closed-form expression for the BER of MIMO FSO systems using ON–OFF keying is derived based on the obtained PDF. The proposed method is validated through comparing the BER results obtained by the analytical calculation and the Monte Carlo simulation.

This paper looks into the throughput performance of a carrier sense multiple access (CSMA) protocol in Weibull fading channels. Following a power capture model, with incoherent addition of interfering signals, upper bounds and lower bounds on the throughput performance are derived analytically. Comparing the upper and lower bounds, it is seen that for propagation delays (normalized by the transmission period) less than one, the bounds are tight on the stable side of the throughput curves, i.e., for mean offered traffic rate G less than G^{*} (the mean offered traffic for which maximum throughput is achieved). In particular, the maximum point on the upper bound is seen to be very close to that on the lower bound, hence providing very tight bounds for the maximum throughput.

The possibility of using modified Weibull distributions for estimation and statistical-physics analysis of the reliability of articles is analyzed. It is proposed that a mixture of distributions – exponential and Weibull distributions – be used.

Channel estimation at the receiver side is essential for adaptive modulation schemes, prohibiting low complexity systems from using variable rate (VR) and/or variable power transmissions. This problem can be solved using variable-rate M-QAM modulation scheme for communications over fading channels in the absence of channel gain estimation at the receiver. It is shown that signal plus noise (S + N) sampling value can serve as a much better criterion compared to signal-to-noise ratio (S/N) for determining modulation order in VR systems. In this way, low complexity transceivers use VR transmissions to improve spectrum efficiency under an error performance constraint. Two kinds of fading channels: Weibull fading and α–μ fading are considered. Spectrum efficiency of (S + N) based systems are compared to that of S/N systems and the advantage of (S + N) scheme over (S/N) scheme is shown. The symbol error rates of two schemes are also studied. As an application, the proposed VR modulation scheme is shown to work with a maximum ratio combining diversity receiver.

In planning and operation of an electric power transmission system, accurate estimation of the reliability of its different components is a fundamental and challenging concern. Two-parameter Weibull probability distribution has been used frequently for this purpose. However, this model cannot capture all behaviours of the many different components in a transmission system. Over the years several alternative models have been proposed that are either derived from, or in some way related to, the two-parameter Weibull distribution. However, these alternatives have received little attention in reliability analysis of power transmission systems. It seems the lack of a simple and applicable guideline for model selection and validation is one of the main impediments. Many of these derived distributions (Weibull distribution family) have characteristic shape in the Weibull probability plot (WPP). Hence, WPP can be used as a tool for model selection and validation through the Weibull distribution family. This paper provides a WPP-based guideline and flowchart for selection of the most appropriate Weibull method. The application of the guideline is demonstrated by a case study using historical data of power transformer.

Fading is the most observed and frustrating problem in transmitting and receiving radio signals. A Study in correlation properties of fading helps to design proper communication systems that are robust to it. In this work, received power signal was obtained by drive-test technique. The analysis was determined using distribution fitting tool in Matlab software 7.5.0 (R2007b). The following fading distributions were used, Rayleigh, Rician, Nakagami-m, Lognormal and Weibull. Weibull fading distribution was found to give the best description of fading experienced in Ghana.On the other hand, Rician distribution, Nakagami-m distribution and lognormal distribution have less agreement with the measured data while Rayleigh fading distribution has much less agreement with measured data. The obtained mean scale parameter and the mean shape parameter in the Weibull distribution for the environment considered were 133.76 and 15.93, respectively. Furthermore, the path loss exponents in the near and far fields were also calculated; and the standard deviation of shadowing fell in the range of 4.368dB to 6.180dB.

The Weibull distribution is widely used in applications such as reliability and lifetime studies. Although this distribution has three parameters, for simplicity, literature pertaining to Weibull parameter estimation relaxes one of its parameters in order to estimate the other two. When the three-parameter Weibull distribution is of interest, the estimation procedure is complicated. For example, the likelihood function for a three-parameter Weibull distribution is hard to maximize. In this paper, a Cross Entropy (CE) method is developed in the context of maximum likelihood estimation (MLE) of a three-parameter Weibull distribution. Performing a simulation study, a comparative analysis between the newly developed method and two existing methods is conducted. The results show the proposed method has better performance in terms of accuracy, precision and run time for different parameter settings and sample sizes.

The performance of two-way amplify-and-forward (AF) cooperative relay networks over independent but not necessarily identically distributed Weibull fading channels is studied. Tight closed form approximations for the overall outage probability (OOP) and the average symbol error probability (ASEP) are derived. The analysis is verified by simulation, and the accuracy is shown to be excellent, especially at high signal noise ratio (SNR). According to the analysis, increasing the fading parameter, the power scaling parameter, or the number of relays, can improve the system performance when the best relay is selected.

U ovom radu je razmotren bežični telekomunikacijski sustav sa SC prijemnikom koji radi u prisustvu Weibull-ovog fedinga i Gamma sjenke. Utjecaj Weibull-ovog fedinga na primljeni signal se ogleda u promjeni anvelope signala, a utjecaj Gamma sjenke u promjeni snage izlaznog signala. SC prijemnik se koristi za smanjenje utjecaja fedinga i sjenke na karakteristike sustava. Izraz za srednji broj osnih presjeka izlaznog signala iz SC prijemnika je izveden u zatvorenom obliku. Dobiveni rezultati se mogu koristiti za izračunavanje prosječnog trajanja otkaza bežičnog sustava. Numerički rezultati su predstavljeni grafički, kako bi se prikazao utjecaj parametara fedinga i sjenke na karakteristike sustava., The wireless telecommunication system consisting of selection combining (SC) receiver which works in Gamma shadowed Weibull multiple-faded channel is discussed in this work. The received signal suffers Weibull small scale fading which leads in variation of the signal envelope and Gamma large scale fading which results in variation of the SC receiver output signal envelope power. SC receiver is utilized to abate the impact of Gamma large scale fading effects and Weibull small scale fading effects on system characteristics. The formula for average level crossing rate (LCR) of signal envelope at SC combiner output is performed in the closed shape. The result we get can be applied to calculate the average fade duration (AFD) of such wireless systems. The obtained solutions are plotted in a few graphs to point out the impact of Weibull fading envelope severity parameter and Gamma shadowing severity parameter on system features.

The analysis and modeling of lifetime data are crucial in almost all applied sciences including medicine, insurance, engineering, behavioral sciences and finance, amongst others. The main objective of this paper is to have a comparative study of two-parameter gamma and Weibull distributions for modeling lifetime data from various fields of knowledge. Since exponential distribution is a particular case of both gamma and Weibull distributions and the exponential distribution is a classical distribution for modeling lifetime data, the goodness of fit of both gamma and Weibull distributions are compared with exponential distribution.

Multiple-input multiple-output (MIMO) systems play a great role in improving performance of wireless communication system and are commonly used to ensure high bit-rate transmission. Space-time block codes (STBC) are a remarkable modulation scheme discovered recently for the multiple antenna wireless channel. They have an elegant mathematical solution for providing full diversity over the coherent, flat-fading channel. In this paper, a method for approximating the probability distribution of sum of independent and identical Weibull random variables is adopted to derive a tight analytical expressions for various performance criteria of STBC's coding operating under identical and independent Weibull fading channels (WFC). The proposed Analytical expressions are given in terms of simple, gamma and Fox-H functions. These expressions demonstrate the best fit to simulation results using Monte-Carlo simulation and other statistical methods.

Many models with three parameters have been developed based on extension or generalization of the Weibull distribution. These models include modified Weibull, Weibull extension, extended Weibull and others. Seven such models are discussed in this paper, in addition to a generalization of the exponential distribution, and a flexible Weibull model with two parameters. These models are more flexible than the usual 2-parameter Weibull, and they are useful for modeling lifetime/failure data with different behaviors such as decreasing, increasing, bathtub-shaped, or even upside-down bathtub-shaped failure rate. In this paper, a procedure for selecting an optimal model for lifetime data analysis is presented based on the plots on Weibull probability paper (WPP). An example is provided to illustrate the procedure and the usefulness of these models. This procedure serves as a guideline for reliability engineers and statisticians when dealing with data modeling.

Recently, the theory of effective rate has attracted much attention, since it can take the delay aspect into account when performing channel capacity analysis. Weibull fading model is a flexible and practical model for describing fading channels in both indoor and outdoor environments. This letter derives the exact analytical expressions of effective rate over independent but not necessarily identical Weibull fading channels, which can be used in the system analysis in real-time communication scenarios. In addition, the closed-form asymptotic expressions under high signal-to-noise ratio (SNR) and low-SNR regimes are derived to provide useful insights into the effects of system and fading parameters on the effective rate.

Reliability analysis is quite important in the facility failure and equipment life studies, and the Weibull distribution is the most common model in the reliability analysis. Therefore, the effective identification of the Weibull model parameters of the facilities has significant importance in the reliability analysis. In this paper, a united estimation method combining probability weighted moments and maximum likelihood estimation is proposed, and the estimation model of Weibull distribution parameters is established. The modified artificial bee colony algorithm introducing Chaos intelligent search strategy and differential evolution operator is used for the estimation model solution. The analysis result shows that MABC has better optimization capability, and the proposed method has the advantages of high precision and strong stability.

Weibull distribution is widely used for modeling the wind speed data in literature. However, in real life, the wind speed data may not always be modeled by using the Weibull distribution. In other words, it may not represent all wind speed characteristic encountered in nature. Therefore, the alternative distributions are used in such cases. In this study, the Inverse Weibull (IW) distribution is used to model the wind speed. First, the modified maximum likelihood (MML) estimators of the parameters of IW distribution are obtained. Then the efficiencies of the MML estimators are compared with the well-known maximum likelihood (ML) and the least squares (LS) estimators via Monte-Carlo simulation study. Simulation results show that the LS estimators are the least efficient among the others. Finally, Weibull and IW distributions are used for modeling the seasonal wind speed data sets obtained from the Turkish State Meteorological Service. It is shown that IW distribution based on the ML and the MML estimates of the parameters provides better modeling than the Weibull distribution based on the corresponding estimates in most of the cases. The suitability of these distributions is compared with respect to root mean square error (RMSE) and coefficient of determination (R-2) criteria. (C) 2016 Elsevier Ltd. All rights reserved.

Spectrum sensing is an important task to find out the spectrum holes in a given radio spectrum. Spectrum sensing performance is improved with aid of multiple cognitive radios (CRs) in the network and each CR having multiple antennas. In this paper, we are considering that each CR having multiple antennas and improved energy detector (IED) is used for detection of primary user (PU). We have derived the novel expression for missed detection probability (P m ), closed form of equations to find out optimum value of number of CR users (N opt ), optimum value of normalized threshold value (λ n, opt ) and optimum value of arbitrary power of the received signals (popt) under Weibull fading channel. Performance is evaluated in terms of total error for various values of SNR & normalized threshold, optimizing the network parameters such as number of CR users (N), normalized threshold value (λ) and arbitrary power (p) of received signals of a PU. It is also observed that performance is improved by using multiple antennas at each CR. Comparison between Rayleigh fading and Weibull fading channels are also provided.

The two-parameter Weibull has been the most popular distribution for modeling lifetime data. We propose a four-parameter gamma extended Weibull model, which generalizes the Weibull and extended Weibull distributions, among several other models. We obtain explicit expressions for the ordinary and incomplete moments, generating and quantile functions and mean deviations. We employ the method of maximum likelihood for estimating the model parameters. We propose a log-gamma extended Weibull regression model with censored data. The applicability of the new models is well justified by means of two real data sets.

This paper analyzes and evaluates the statistical properties of the rms delay spread (delay spread) in a two-path simulcast environment and same frequency in cell repeater. Each path is subjected to multipath fading characterized by wideband Weibull distribution. A novel, unified, and accurate analytical expressions for the probability density function, the mean, the mean square, and the standard deviation for the delay spread have been derived. The derived expressions are then used to study the implication of the fading and scale parameters on the statistical characteristics of the delay spread. To validate the accuracy of the derived formulas, the analytical results are compared with Monte-Carlo simulation results. Full agreement has been noticed between the simulated and the analytical results over a wide range of received signals levels ratio and different values of the fading parameters.

A lifetime distribution model is usually inappropriate for modeling the times between successive failures (TBF) of a repairable system since the TBFs are generally not independent and identically distributed. Traditional methods for modeling the failure process of repairable systems focus on fitting the mean cumulative function (MCF) to a parametric model such as the power-law model. However, the fitted model does not directly provide the distribution of the time to the next failure at a given system age or failure event. To address this issue, we propose a Weibull model with constant shape parameter and time-varying scale parameter for modeling TBFs of a repairable system in this paper. It includes the Weibull distribution as its special case. Three specific parametric models for the scale parameter are developed. The models are suitable for the situations where the system's MTBF can be monotonic or bathtub-shaped, and bounded. Such a model can be viewed as a Weibull process model. Potential applications of the models include modeling manufacturing defect occurrence processes and evaluating the effectiveness of maintenance. Three real-world examples are included to illustrate the appropriateness and usefulness of these models.

The Weibull distribution is a useful statistical model that can be used to describe the multipath fading in nowadays wireless communication environments. In this paper, the bit error rate (BER) performance of Low-Density Parity-Check (LDPC) coded communication systems using different decoding rules is presented over Weibull fading channels by means of comparative computer simulations. It is shown that, especially for the case of the Belief Propagation (BP) decoding rule, significant performance improvement can be achieved in comparison with uncoded transmission when the channel is assumed to have Weibull fading. © 2016 Universidad Nacional Autónoma de México, Centro de Ciencias Aplicadas y Desarrollo Tecnológico., This work was supported by the Research Fund of Erciyes University , grant number: FBD-10-3092 . The authors thank to Proofreading & Editing Office of Erciyes University for careful reading and corrections on the manuscript.

In this paper, we study the performance of energy detection for spectrum sensing over α-μ (a rewritten form of the Stacy or the generalized gamma) fading channels, following a Bayesian approach. We derive an infinite series expression for the probability of error, which is a convex combination of probabilities of false-alarm and signal detection. Also, we present an analysis on the optimal detection threshold that minimizes the probability of error. The analysis is validated through Monte Carlo simulations, and the performance of the detector for different values of the parameters α and μ are discussed. The derived results are useful as the α-μ fading distribution includes several practical fading models such as Rayleigh, Nakagami-m, and Weibull distributions, as special cases.

In this paper, the information-theoretic secrecy of Weibull fading channels is investigated. The present work is a generalization of the analysis on Rayleigh fading. This paper focuses on the scenario that the channel state information is available to the legitimate transmitter. The cases of single and multiple eavesdroppers are discussed. Several formulas of the average secrecy capacity are derived. Profile examples are illustrated and discussed.

We present capacity analysis for multiple-input multiple-output (MIMO) system under a low signal-to-noise ratio (SNR) regime. We have selected a composite fading channel that considers Weibull fading for multipath and gamma fading for shadowing. We have presented the analysis in a detailed form for three different techniques, namely, spatial multiplexing (SM) with optimal detection, SM with minimum mean square error (MMSE) detection, and orthogonal space-time block codes (OSTBC). Because capacity analysis at arbitrary signal-to-noise (SNR) is stringent, a low SNR regime is considered to achieve a positive rate and wideband slope. The improvement is the result of minimizing energy per information bit (Eb). For the first time, closed-form expressions are evaluated for the capacity of MIMO systems at low SNR under WG fading channels which facilitate the performance comparison for proposed techniques.

To analyze the reliability of lifetime of products, the Weibull distribution plays a key role in many industries. In the following section, the Weibull distribution is used to predict the fatigue-related lifetime of rolling bearings at any reliable probability statistically.

A five-parameter extension of the Weibull distribution capable of modelling a bathtub-shaped hazard rate function is introduced and studied. The beauty and importance of the new distribution lies in its ability to model both monotone and non-monotone failure rates that are quite common in lifetime problems and reliability. The proposed distribution has a number of well-known lifetime distributions as special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull (MW) distributions, among others. We obtain quantile and generating functions, mean deviations, Bonferroni and Lorenz curves and reliability. We provide explicit expressions for the density function of the order statistics and their moments. For the first time, we define the log-Kumaraswamy MW regression model to analyse censored data. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is determined. Two applications illustrate t...

In wireless communications, cooperative relaying is well-known to enhance the overall system performance, but implementation and cost constraints stand against its wide deployment. This paper investigates the performance of cooperative relays with and without multiple antennas under independent and identically distributed (i.i.d.) Weibull faded channels in a two-hop wireless network. We consider the Weibull fading channel model due to its flexibility in describing the radio propagation environment more than the classical Rayleigh model. Our study relies on applying selection combining (SC) along with threshold decode and forward (TDF) protocol at the cooperative relays as a good compromise between cost and performance. In addition, maximal ratio combining (MRC) is used at the destination. We derive analytical expressions for the end-to-end (E2E) error performance of the network under such scenario and provide simulation results to confirm the validity of the obtained analytical expressions.

With an improved Rayleigh fading model and a zero-mean stochastic sinusoid as the scattering and specular components respectively, a stochastic simulation model is proposed for the generation of Rayleigh and Rician fading waveforms. Compared with the existing stochastic models, the proposed simulator needs only one trial to obtain the desired statistical properties even if the number of samples is not large enough. Moreover, the proposed simulation model can directly generate multiple uncorrelated waveforms for different fading scenarios, such as single-input single-output frequency selective channels and multiple-input multiple-output channels. The performance evaluation and comparison show that the proposed simulator is efficient and accurate.

Clutters are all unwanted radar returns to affect on detection of targets. Radar clutter is characterized by amplitude distributions, spectrum, etc. Clutter is modelled with considering these kinds of characteristics. In this paper, a Weibull distribution function approximated by uniform distribution function is suggested. Weibull distribution function is used to model the various clutters. This paper shows that the data generated by the approximated solution of Weibull distribution function satisfy the Weibull probability density function. This paper shows that the data generation time of approximated Weibull distribution function solution is reduced by 20 % compared with the generation time of original Weibull probability density function.

A generalized version of four parameter modified inverse weibull distribution (MIWD) is introduced in this paper. This distribution generalizes the following distributions: (1) Modified Inverse exponential distribution, (2) Modified Inverse Rayleigh distribution, (3) Inverse weibull distribution. We provide a comprehensive description of the mathematical properties of the modified inverse weibull distribution along with its reliability behaviour. We derive the moments, moment generating function and examine the order statistics. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. The inverse weibull distribution is the life time probability distribution which is used in the reliability engineering discipline. The inverse weibull distribution can be used to model a variety of failure characteristics such as infant mortality, useful life and wear-out periods. Reliability and failure data both from life testing and in service records which is often modeled by the life time distributions such as the inverse exponential, inverse Rayleigh, inverse Weibull distributions. In this research we have developed a new reliability model called modified inverse weibull distribution. This paper focuses on all the properties of this model and presents the graphical analysis of modified inverse weibull reliability models. This paper present the relationship between shape parameter and other properties such as non- reliability function, reliability function, instantaneous failure rate, cumulative instantaneous failure rate models. This life time distribution is capable of modeling of various shapes of aging and failure criteria.The proposed model can be used as an alternative to inverse generalized exponential, inverse generalized Rayleigh, inverse generalized weibull distributions. The cumulative distribution function (CDF) of the Inverse weibull distribution is denoted by

Maximum likelihood estimation (MLE) is a commonly used method of Weibull distribution, but it needs to calculate the transcendental equations which is based on the computer programming. In this paper, we established a new MLE model of Weibull distribution in a case of random censoring. And this model was proved feasible and correct via three examples. At the same time, the model can be used for a variety of censored data and complete life data of Weibull distribution of MLE.