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Statistical analysis of the time-to-event scenarios commonly involves the use of the exponential and Rayleigh distributions. However, the exponential distribution is constrained by its constant failure rate, while the Rayleigh distribution exhibits a growing (or increasing) failure rate. The linear failure rate distribution provides a broader perspective by encompassing both of these distributions, including the possibility of a non-increasing hazard function. In this paper, a new distribution is introduced, which could be considered as one of the major modifications to the linear failure rate distribution, known as the weighted linear failure rate distribution. The model proposed illustrates both monotonic and a known non-monotonic failure rate. This paper extensively explores the characteristics of the proposed distribution. It presents the maximum likelihood estimates for the unknown parameters and includes a simulation study. The analysis focuses on three real data sets obtained from the fields of musical education and engineering. By employing three decisive tools, it is observed that the current distribution provides a superior fit in comparison to several other widely recognized distributions. [ABSTRACT FROM AUTHOR]

In today's security landscape, the proliferation of unauthorized drones in restricted airspace has emerged as a significant threat. These drones pose various risks, from potential surveillance and espionage to more sinister possibilities such as physical attacks. Consequently, the development of effective anti-drone laser systems has become increasingly vital. Our study focuses on three main objectives: modeling internal reliability, identifying critical components, and studying the factors affecting the reliability of anti-drone systems. We aim to enhance the overall performance and effectiveness of anti-drone laser systems by analyzing the reliability of critical components and understanding how system parameters influence system reliability. To this end, reliability block diagram (RBD) methodology has been employed to compute the reliability of the laser subsystem in the anti-drone system. Additionally, we conduct a comprehensive review of component-wise reliability to identify vulnerable points within the system, thus enabling targeted improvements and optimizations. To capture the realistic scenario of system failure behavior, different distributions have been used to compute the reliability of the system, ensuring a thorough understanding of its operational reliability in diverse conditions. Finally, the energy values and probability of hitting are obtained for the anti-drone laser system to effectively mitigate environmental challenges. [ABSTRACT FROM AUTHOR]

This study introduces a negative Rayleigh detection model for estimating population abundance in line transect surveys. The model satisfies key detection conditions and provides a detailed analysis of its probability density function, moments, and other essential characteristics. Parameters are estimated using three methods: moment estimator, maximum likelihood estimator, and Bayesian estimator. The model's performance is evaluated through simulations, comparing its estimators to those from established models. An empirical application using perpendicular distance data further assesses the model, with goodness-of-fit statistics demonstrating its advantages over traditional methods. [ABSTRACT FROM AUTHOR]

This study seeks for classical estimations to estimating the anonymous parameters and reliability function of Modified Weighted Exponential Rayleigh MWER distribution. These classical methods are chosen precisely because all of these methods maximize the probability density function. Newton-Raphson technique was used to derive estimation methods. [ABSTRACT FROM AUTHOR]

The main aim of this research is to analyze the characteristics of the wind speed and wind power density in Baghdad City within micro-scale meteorological conditions at Mustansiriyah University Meteorological Station (MUMS). Temperature, atmospheric pressure and wind speed data were taken for one year (2016) measured at a height of 18 m above the earth's surface. Hourly, monthly, and seasonal changes in wind speed at an altitude of 30 m were estimated using a power law. The mean diurnal and monthly air density was calculated. Different statistical distributions were used, including the Rayleigh, Gamma and Weibull distributions, and the best distribution function was selected to evaluate the wind power density in the study area. The results showed the highest monthly mean of wind speed recorded in June and July. Therefore, these months have the highest wind power density. The lowest monthly mean of wind speed and wind power density was observed in December. The maximum and minimum values of air density were recorded in December, January and July, August, respectively. The monthly variation of the shape parameter (k) ranges between 0.99 - 1.81, while the monthly variation of the scale parameter(c) ranges between 1.07 - 2.3 m s-1. It was also found that the Weibull distribution was more accurate than the Rayleigh and Gamma distributions. The prevailing wind direction is northeast (NE) and east-northeast (ENE) most of the time. The research results showed that the study area is not suitable for using wind energy to generate energy. [ABSTRACT FROM AUTHOR]

It has been widely acknowledged that probability-based methodologies play a crucial role in guiding decision-making processes when faced with uncertain or vague circumstances. To ensure that decisions made under such conditions are both meaningful and productive, a variety of methodologies centered around probability have been developed, endorsed, and put into practice. This study also aims to contribute to the existing body of knowledge by introducing a new probability model known as the weighted sine generalized Rayleigh distribution. For the proposed model, certain properties are derived. Furthermore, the parameter estimation technique and simulation studies based on the proposed model are also presented. Finally, the proposed model is successfully implemented on three distinct data sets sourced from sports and different engineering disciplines. By evaluating the statistical significance through the p-value and other various tests, it is evident that the proposed model consistently outperforms its competitor distributions. The practical illustration, emphasizes the efficacy and potential of the proposed model for widespread applications in sports and engineering research and practice.

Statistical analysis of the time-to-event scenarios commonly involves the use of the exponential and Rayleigh distributions. However, the exponential distribution is constrained by its constant failure rate, while the Rayleigh distribution exhibits a growing (or increasing) failure rate. The linear failure rate distribution provides a broader perspective by encompassing both of these distributions, including the possibility of a non-increasing hazard function. In this paper, a new distribution is introduced, which could be considered as one of the major modifications to the linear failure rate distribution, known as the weighted linear failure rate distribution. The model proposed illustrates both monotonic and a known non-monotonic failure rate. This paper extensively explores the characteristics of the proposed distribution. It presents the maximum likelihood estimates for the unknown parameters and includes a simulation study. The analysis focuses on three real data sets obtained from the fields of musical education and engineering. By employing three decisive tools, it is observed that the current distribution provides a superior fit in comparison to several other widely recognized distributions.

In this paper, we propose bivariate iterated Farlie–Gumbel–Morgenstern (FGM) due to [Huang and Kotz (1984). Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions. Biometrika 71(3), 633–636. https://doi.org/10.2307/2336577] with Rayleigh marginals. The dependence stress–strength reliability function is derived with its important reliability characteristics. Estimates of dependence reliability parameters are obtained. We analyse the effects of dependence parameters on the reliability function. We found that the upper bound of the positive correlation coefficient is attaining to 0.41 under a single iteration with Rayleigh marginals. A comprehensive comparison between classical FGM with iterated FGM copulas is graphically examined to assess the over or under estimation of reliability with respect to α and β. We propose a two-phase estimation procedure for estimating the reliability parameters. A Monte-Carlo simulation study is conducted to assess the finite sample behaviour of the proposed reliability estimators. Finally, the proposed estimators are examined and validated with real data sets.

Estimating a common parameter is the most essential and quite fascinating task across various probability distributions. This article addresses the challenge of estimating this parameter through the application of Maximum Likelihood Estimation (MLE). Numeric determination of common parameters is conducted for several distributions, including the Lomax distribution, Gamma distribution, Rayleigh distribution, and Weibull distribution. In cases where distributions lack a closed-form solution, estimation of MLEs is achieved using the Newton-Raphson technique. Furthermore, asymptotic confidence intervals are computed utilizing the Fisher information matrix tailored to each distribution. The performance evaluation of these estimators centers on the assessment of bias and mean squared error. To enable a numerical comparison of these estimators, the Monte Carlo simulation method is employed. Finally, these techniques are applied to real-time rainfall data to assess parameter estimates for each distribution.

The proliferation of solar panel installations presents significant societal and environmental advantages. However, many panels are situated in remote or inaccessible locations, like rooftops or vast desert expanses. Moreover, monitoring individual panel performance in large-scale systems poses a logistical challenge. Addressing this issue necessitates an efficient surveillance system leveraging wide area networks. This paper introduces an Internet of Sensing Things (IoST)-based monitoring system integrated with sun-tracking capabilities for solar panels. Cutting-edge sensors and microcontrollers collect real-time data and securely store it in a cloud-based server infrastructure, enabling global accessibility and comprehensive analysis for future optimization. Innovative techniques are proposed to maximize power generation from sunlight radiation, achieved through continuous panel alignment with the sun's position throughout the day. A solar tracking mechanism, utilizing light-dependent sensors and servo motors, dynamically adjusts panel orientation based on the sun's angle of elevation and direction. This research contributes to the advancement of efficient and sustainable solar energy systems. Integrating state-of-the-art technologies ensures reliability and effectiveness, paving the way for enhanced performance and the widespread adoption of solar energy. Additionally, the paper explores anomaly prediction using Rayleigh distribution, offering insights into potential irregularities in solar panel performance. [ABSTRACT FROM AUTHOR]

Accurately extracting and segmenting boundaries between targets and backgrounds is difficult in Synthetic Aperture Radar (SAR) images because of the many scattering mechanisms that produce echo signals. These complications combined with the ubiquitous speckle noise present in SAR images cause traditional segmentation algorithms to frequently produce unacceptable results. In order to tackle these problems, we provide a unique segmentation strategy that makes use of a minimum error thresholding technique based on the theory of the Rayleigh distribution. Our technique builds a local translation Rayleigh model by utilizing the stationary wavelet domain, which successfully suppresses speckle noise and generates SAR images that are easier to segment. Next, we utilize a two-dimensional entropy thresholding method to segment images. We present a variable code length genetic technique that incorporates the optimization of segmentation category numbers encoded in the chromosomes into the fitness function in order to further improve segmentation performance. Furthermore, our method yields minimum segmentation error pixels and excellent segmentation efficiency since the segmentation thresholds it finds is accurate. By addressing major issues with speckle noise and segmentation precision, this enhanced approach provides notable improvements in the precise and effective segmentation of SAR images. [ABSTRACT FROM AUTHOR]

Estimating a common parameter is the most essential and quite fascinating task across various probability distributions. This article addresses the challenge of estimating this parameter through the application of Maximum Likelihood Estimation (MLE). Numeric determination of common parameters is conducted for several distributions, including the Lomax distribution, Gamma distribution, Rayleigh distribution, and Weibull distribution. In cases where distributions lack a closed-form solution, estimation of MLEs is achieved using the Newton-Raphson technique. Furthermore, asymptotic confidence intervals are computed utilizing the Fisher information matrix tailored to each distribution. The performance evaluation of these estimators centers on the assessment of bias and mean squared error. To enable a numerical comparison of these estimators, the Monte Carlo simulation method is employed. Finally, these techniques are applied to real-time rainfall data to assess parameter estimates for each distribution. [ABSTRACT FROM AUTHOR]

Copyright of Baghdad Science Journal is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Multiple-input multiple-output (MIMO) technologies use multiple antennas at the sender and the receiver to get the high data rate that the next-generation communication system needs. This paper compares MIMO systems using the Quadrature Phase Shift Keying (QPSK) modulation scheme for two-channel distributions of Rayleigh and Weibull types. The performance of the work is far with the Minimum Mean Square Equalizer (MMSE) in terms of Bit Error Rate (BER) for various antenna number situations on the transmitter and receiver sides. The MIMO module is carried out using MATLAB code. The channel noise will be a signal of random noise that is generated. To mitigate the impact of interchannel interference, the MMSE approach employs inverse filtering at the receiver, and BER will be calculated. According to simulation results, the system's performance is primarily influenced by the number of antennas; it decreased as the number of antennas increased, and the BER of the Weibull channel decreased as the two-parameter value increased. [ABSTRACT FROM AUTHOR]

The main aim of this research is to analyze the characteristics of the wind speed and wind power density in Baghdad City within micro-scale meteorological conditions at Mustansiriyah University Meteorological Station (MUMS). Temperature, atmospheric pressure and wind speed data were taken for one year (2016) measured at a height of 18 m above the earth's surface. Hourly, monthly, and seasonal changes in wind speed at an altitude of 30 m were estimated using a power law. The mean diurnal and monthly air density was calculated. Different statistical distributions were used, including the Rayleigh, Gamma and Weibull distributions, and the best distribution function was selected to evaluate the wind power density in the study area. The results showed the highest monthly mean of wind speed recorded in June and July. Therefore, these months have the highest wind power density. The lowest monthly mean of wind speed and wind power density was observed in December. The maximum and minimum values of air density were recorded in December, January and July, August, respectively. The monthly variation of the shape parameter (k) ranges between 0.99 - 1.81, while the monthly variation of the scale parameter(c) ranges between 1.07 - 2.3 m s-1. It was also found that the Weibull distribution was more accurate than the Rayleigh and Gamma distributions. The prevailing wind direction is northeast (NE) and east-northeast (ENE) most of the time. The research results showed that the study area is not suitable for using wind energy to generate energy.

The design innovations in the extraction of urban impervious surfaces have played a vital role in using Very High-Resolution Synthetic Aperture Radar technology. Advanced radar technologies are integrated here, with the inclusion of various statistical methodologies like Rayleigh, Nakagami and K- distributions in integration with the Gray Level Co-occurrence Matrix, Principal Component Analysis and Gabor filters. For analyzing the intensity data of SAR imagery in regard to environmental monitoring, as well as Electronic Warfare has been used in the research. The Shapiro-Wilk test shows the beginning of this work; investigating the departure from normality, the material properties and environmental factors were viewed to have a significant effect on the variation in pixel intensities. Further, the analysis of data with heterogeneity based on some measures of Skewness and Kurtosis was performed. This research is based on design-centred approaches for reducing state noise and enhancing target tracking in complex scenarios by performing textural analysis using techniques such as GLCM, PCA and Kalman filtering. Integration optimizes VHR SAR for enhanced situational awareness and effective detection in an urban landscape. This therefore places a great magnitude on the influence of design on the modification of material properties and effective radar detection. [ABSTRACT FROM AUTHOR]

In this research paper, confidence interval using maximum likelihood estimation is obtained for Poisson type Rayleigh class for the parameters. The failure intensity function, mean time to failure function and likelihood function for the parameter is derived. Confidence interval has been obtained for the parameters using maximum likelihood estimation. To study the performance of proposed Confidence interval, average length and coverage probability are calculated by using Monte Carlo simulation technique. From the obtained intervals, it is concluded that Confidence interval for the parameters perform better for appropriate choice of execution time and certain values of parameters. [ABSTRACT FROM AUTHOR]

In this manuscript, a new probability model named as Sine Power Rayleigh distribution (SPRD) is proposed using a Sine-G function as generator. Various statistical properties of this new distribution were investigated, including the survival function, hazard function, reverse hazard rate, cumulative hazard function, mills ratio, quantile function, moments, moment generating function, conditional moments, entropy, and order statistics. The parameters of the proposed distribution were estimated using the method of maximum likelihood estimation. To assess the model's versatility and applicability, we conduct analyses on two real life data sets. The outcomes affirm the superior performance of the newly proposed model SPRD as compared to existing models. [ABSTRACT FROM AUTHOR]

Multiple-input multiple-output (MIMO) technologies use multiple antennas at the sender and the receiver to get the high data rate that the next-generation communication system needs. This paper compares MIMO systems using the Quadrature Phase Shift Keying (QPSK) modulation scheme for two-channel distributions of Rayleigh and Weibull types. The performance of the work is far with the Minimum Mean Square Equalizer (MMSE) in terms of Bit Error Rate (BER) for various antenna number situations on the transmitter and receiver sides. The MIMO module is carried out using MATLAB code. The channel noise will be a signal of random noise that is generated. To mitigate the impact of inter-channel interference, the MMSE approach employs inverse filtering at the receiver, and BER will be calculated. According to simulation results, the system's performance is primarily influenced by the number of antennas; it decreased as the number of antennas increased, and the BER of the Weibull channel decreased as the two-parameter value increased

This study aims to statistically analyze wind speed data of Tarnab, Peshawar, for the period 2004-2023. The data was recorded at the Agriculture Research Institute, Tarnab, Peshawar. Two statistical models (two-parameter Weibull and Rayleigh distribution functions) were applied to find the distributions of wind speeds. For the estimation of shape and scale parameters of Weibull and Rayleigh, two methods were employed: the method of moments and the energy pattern factor. Three statistical tools (mean percentage error, mean absolute percentage error, and root mean square deviation) were applied to check the error percentage of both models. The results of the Weibull distribution were much closer to the observed data than those of the Rayleigh distribution. The average values of wind speeds tended to increase from winter to summer and vice versa. The highest recorded annual and seasonal wind speeds were 26.19 in/s and 41.57 in/s, respectively, while the lowest values were 7.11 in/s and 4.95 in/s, respectively. Thus, while ruling out the possibility of harnessing wind as a significant source of energy, the findings are still useful for the crops produced in the region.

Abstract In this study, wind characteristics and electricity generation potential from wind energy were investigated in the Bitlis‐Rahva region in eastern Turkey. Ten‐minute wind data from the Bitlis meteorological station were used in the study. The determination of the wind speed (WS) distribution was carried out using the WindPRO program together with the Weibull and Rayleigh distributions. R2, RMSE, and χ2 goodness‐of‐fit tests were used to measure the accuracy of the velocity distribution process. A digital elevation model of the power generation site was created to evaluate wind data and predict turbine performance. Wind power generation performance was evaluated using five different wind turbines (WTs). A power curve model was developed for the WTs to determine the capacity for energy generation. According to the error tests, it has been determined that the results obtained with the WindPRO program can represent the observed wind data most accurately. The results from the WindPRO program analysis showed an average annual WS of 3.26 m/s and a power density of 49.77 W/m2. Increasing height was found to increase WS and power density. The prevailing wind direction was found to be South‐Southwest with a frequency value of 27.5%. The largest capacity factor was obtained from the WT with the largest rotor diameter and rated power. Out of all the WTs examined, the turbine with the largest rated power and rotor diameter produced the greatest amount of energy. According to the capacity factor values calculated for the selected WTs, the region is not considered efficient for wind energy investments. However, as WS and power density increase with increasing altitude, it is thought that different higher parts of the region may be more efficient in terms of wind energy utilization.

The lifetime performance index is a process capability index that is commonly used for the evaluation of the durability of products in life testing and reliability analysis. In the context of multiple production lines, we introduce an overall lifetime performance index and explore the relationship between this comprehensive index and individual lifetime performance indices. For products with lifespans following the Rayleigh distribution in the ith production line, we delve into the maximum likelihood estimator and asymptotic distribution to derive both the individual and overall lifetime performance indices. By establishing a predetermined target for the overall lifetime performance index, we can determine the corresponding target for each individual lifetime performance index. The testing algorithmic procedure is proposed to ascertain whether the overall lifetime performance index has reached its target value based on the maximum likelihood estimator, accompanied by figures illustrating the analysis of test power. We found that there is a monotonic relationship for the test power with various structures of parameters. Finally, a practical illustration with one numeral example is presented to demonstrate how the testing procedure is employed to evaluate the capabilities of multiple production lines. [ABSTRACT FROM AUTHOR]

In recent years, wind energy has become remarkably popular among renewable energy sources due to its low installation costs and easy maintenance. Having high energy potential is of great importance in the selection of regions where wind energy investments will be made. In this study, the wind power potential in Çanakkale Province, located in the northwest of Türkiye, is examined, and the wind speed is estimated using hourly and daily data over a one-year period. The data, including 12 different meteorological parameters, were taken from the Turkish State Meteorological Service. The two-parameter Weibull and Rayleigh distributions, which are the most widely preferred models in wind energy studies, are employed to estimate the wind power potential using hourly wind speed data. The graphical method is implemented to calculate the shape (k) and scale (c) parameters of the Weibull distribution function. Daily average wind speed estimation is performed with artificial neural network–genetic algorithm (ANN-GA) and ANN–particle swarm optimization (ANN-PSO) hybrid approaches. The proposed hybrid ANN-GA and ANN-PSO algorithms provide correlation coefficient values of 0.94839 and 0.94042, respectively, indicating that the predicted and measured wind speed values are notably close. Statistical error indices reveal that the ANN-GA model outperforms the ANN-PSO model. [ABSTRACT FROM AUTHOR]

It is shown that very steep coastal profiles can give rise to unexpectedly large wave events at the coast. We conduct a statistical analysis of runs from a nearshore Boussinesq-type model to demonstrate that under certain wave conditions, which a casual observer would perceive as calm, the likelihood of large run-up events is uncharacteristically high. The data computed by the Boussinesq-type model show that sea states with lower overall wave steepness favor higher run-up. Under these wave conditions, more of the available wave energy reaches the shore, since less wave breaking occurs, which can create a false sense of security for beach-goers. [ABSTRACT FROM AUTHOR]

Copyright of Basrah Journal of Science / Magallat Al-Barat Li-L-ulum is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this study, wind characteristics and electricity generation potential from wind energy were investigated in the Bitlis‐Rahva region in eastern Turkey. Ten‐minute wind data from the Bitlis meteorological station were used in the study. The determination of the wind speed (WS) distribution was carried out using the WindPRO program together with the Weibull and Rayleigh distributions. R2, RMSE, and χ2 goodness‐of‐fit tests were used to measure the accuracy of the velocity distribution process. A digital elevation model of the power generation site was created to evaluate wind data and predict turbine performance. Wind power generation performance was evaluated using five different wind turbines (WTs). A power curve model was developed for the WTs to determine the capacity for energy generation. According to the error tests, it has been determined that the results obtained with the WindPRO program can represent the observed wind data most accurately. The results from the WindPRO program analysis showed an average annual WS of 3.26 m/s and a power density of 49.77 W/m2. Increasing height was found to increase WS and power density. The prevailing wind direction was found to be South‐Southwest with a frequency value of 27.5%. The largest capacity factor was obtained from the WT with the largest rotor diameter and rated power. Out of all the WTs examined, the turbine with the largest rated power and rotor diameter produced the greatest amount of energy. According to the capacity factor values calculated for the selected WTs, the region is not considered efficient for wind energy investments. However, as WS and power density increase with increasing altitude, it is thought that different higher parts of the region may be more efficient in terms of wind energy utilization. [ABSTRACT FROM AUTHOR]

In this research, the reliability functions are applied to estimate the hazard function of four used car components such as (tires, brakes, lights, and engine), which are inspected by aperiodic vehicle inspection (PVI) established in Erbil city, a specialized company that conducts the annual technical inspection of vehicles to detect the failure component, that either require repair or replace it with a new one. For our purpose, the data about the failure components of a sample of size (50,000) cars are obtained from the Erbil traffic directorate, which are annually inspected for 11 years (2010–2020) by a (PVI) company. From the available data, the reliability function, hazard function, and probability density function of the failure time of each component are found by the non-parametric method and the estimated Rayleigh distribution since the failure rates of the components are the linear functions of time, also the comparison between their reliability values have made by the mean absolute error method. [ABSTRACT FROM AUTHOR]

We develop new goodness of fit tests for Rayleigh distribution based on fixed point characterization. We use U-Statistic theory to derive the test statistics. First we develop a test for complete data and then discuss, how the right censored observations can be incorporated in the testing procedure. The asymptotic properties of the test statistic in both uncensored and censored cases are studied in detail. Extensive Monte Carlo simulation studies are carried out to validate the performance of the proposed tests. We illustrate the procedures using real data sets. We also provide, a goodness of fit test for the standard Rayleigh distribution based on jackknife empirical likelihood. [ABSTRACT FROM AUTHOR]

Working on symmetrical or asymmetrical data is complicated since each requires a different probability density function. Many statistical distributions can be used for these data types, where choosing one should be satisfied with the correct data type. So, we apply the ranked set sampling technique, which is essential in gaining data when dealing with units in a population is expensive. However, their classification is simple according to the variable of interest. The Unit Generalized Rayleigh distribution has recently played a crucial role in analyzing symmetrical or asymmetrical complex data sets specifically in modeling claim and risk data used in actuarial and financial studies, and its density can take different symmetric and asymmetric possible shapes. It is proposed in various areas, such as reliability, survival, economics, actuarial science, and insurance. We applied the ranked set sampling design in this article for gaining the model parameter estimations of the unit generalized Rayleigh model. Different estimation procedures and risk measures are computed. Moreover, the performance of these measures is illustrated via numerical simulation experiments. Under different proposed estimators, we conduct the validation of the suggested ranked set sampling design via numerous Monte Carlo simulation experiments by computing average bias and mean squared errors. At the end, we illustrated two real applications of the financial area for demonstrating the potential and the supremacy of the proposed ranked set sampling estimators.

This paper investigates the estimation of three unknown parameters for the [0, 1] Truncated Nadarajah Haghighi Rayleigh distribution, denoted as ([0, 1] TNHR). It explores eight different estimation methods, namely the maximum likelihood, maximum product spacing, Anderson-Darling, Right Anderson-Darling, ordinary least squares, weighted least squares, Cramer-von Mises, and percentiles for point estimation. Detailed analyses were conducted to compare the effectiveness of these estimators in terms of bias and mean squared errors through extensive simulation experiments. The simulation results indicate that all the estimators perform well according to these criteria and exhibit similar values when the sample size is large. Some statistical properties of the new distribution are also derived. Additionally, the estimators were applied to two real life datasets, and the results of the Kolmogorov-Smirnov statistics were reported for each of them. Finally, the [0, 1] Truncated Nadarajah Haghighi Rayleigh distribution was applied to two real world datasets, its performance was compared to other famous extensions of Rayleigh distribution using four different selection criteria.

This study introduces a negative Rayleigh detection model for estimating population abundance in line transect surveys. The model satisfies key detection conditions and provides a detailed analysis of its probability density function, moments, and other essential characteristics. Parameters are estimated using three methods: moment estimator, maximum likelihood estimator, and Bayesian estimator. The model’s performance is evaluated through simulations, comparing its estimators to those from established models. An empirical application using perpendicular distance data further assesses the model, with goodness-of-fit statistics demonstrating its advantages over traditional methods.

The proliferation of solar panel installations presents significant societal and environmental advantages. However, many panels are situated in remote or inaccessible locations, like rooftops or vast desert expanses. Moreover, monitoring individual panel performance in large-scale systems poses a logistical challenge. Addressing this issue necessitates an efficient surveillance system leveraging wide area networks. This paper introduces an Internet of Sensing Things (IoST)-based monitoring system integrated with sun-tracking capabilities for solar panels. Cutting-edge sensors and microcontrollers collect real-time data and securely store it in a cloud-based server infrastructure, enabling global accessibility and comprehensive analysis for future optimization. Innovative techniques are proposed to maximize power generation from sunlight radiation, achieved through continuous panel alignment with the sun’s position throughout the day. A solar tracking mechanism, utilizing light-dependent sensors and servo motors, dynamically adjusts panel orientation based on the sun’s angle of elevation and direction. This research contributes to the advancement of efficient and sustainable solar energy systems. Integrating state-of-the-art technologies ensures reliability and effectiveness, paving the way for enhanced performance and the widespread adoption of solar energy. Additionally, the paper explores anomaly prediction using Rayleigh distribution, offering insights into potential irregularities in solar panel performance.

The article developed a gating technique that allows us to validate ADS-B data without the necessity to verify using the secondary surveillance radar or multilateration. Probabilistic models of the ADS-B data gating technique, as well as the algorithm for applying these models were proposed. Benchmark cases that occur when aircraft (A/C) positioning by ADS-B systems, determined by threshold values of navigation and pilot’s errors, were analyzed. The first benchmark case assumes not exceeding of navigation and pilot’s errors the bounds of the tolerance limits, which allows us to draw up a conclusion concerning the ADS-B data validation. The second one assumes exceeding of a pilot’s error the bounds of the tolerance limits under an allowable navigational error. Herewith, the air traffic controller (ATC) obtains a message about the proper ADS-B operation and the necessity to issue instructions to the pilot to correct a flight. The third benchmark case assumes exceeding of a navigation error the bounds of the tolerance limits under an allowable or not allowable pilot’s error. In this case, the ATC obtains a message about not valid ADS-B data and the incapability to use these systems. The simulation of the given benchmark cases was performed. In addition, the Rayleigh and Rice distributions were applied to implement the ADS-B data gating technique. The simulation results allow us to assess the required amount of accumulated ADS-B data for the evaluation. Thus, it was found that during the estimate based on the Rayleigh distribution, it is sufficient to accumulate 15–20 measurements, which, when transmitting 2 messages per second and under the condition of the normal ADS-B equipment operation, will take 8–10 s. During the estimate, using the Rice distribution, an accumulation of 25–30 measurements is sufficient, which will take 13–20 s. The developed method will allow the use of ADS-B systems at regional aerodromes with the low intensity of air traffic as the primary or sole surveillance means.

This study focuses on a novel family of distributions inspired by the hyperbolic sine function. The Rayleigh distribution is the base model for the newly formed family of distributions known as the new hyperbolic Sine-Rayleigh distribution. The recommended distribution’s distinct structural traits have been examined. The behaviors of the distributional functions of the proposed model are depicted in several figures. The maximum likelihood estimation procedure is employed to estimate the specified distribution parameters. A simulation study was carried out to examine and evaluate the behavior of the estimators. Moreover, the efficacy of the specified distribution is supported by realistic data sets pertaining to engineering science.

The unstable nonlinear Schrödinger equation (UNLSE) characterises the time evolution of disturbances through unstable or marginally stable media. We study the stochastic UNLSE and stochastic modified UNLSE (mUNLSE). We apply the unified solver to provide some new stochastic solutions via Rayleigh distribution. The gained stochastic solutions play a crucial role in nonlinear sciences. Rayleigh distribution is used to depict the dispersion random input. In light of description of the behaviour of stochastic solutions, their mean and variance are illustrated. We show the influence of random parameters on the gained stochastic solutions. With the aid of Maple software, various profile pictures are introduced to exhibit the dynamical behaviour of the stochastic solutions. [ABSTRACT FROM AUTHOR]

In this work, we study the possibility of using a new non-homogeneous stochastic diffusion process based on the Rayleigh density function to model the evolution of the active cases of COVID-19 in Morocco. First, the main probabilistic characteristics and analytic expression of the proposed process are obtained. Next, the parameters of the model are estimated by the maximum likelihood methodology. This estimation and the subsequent statistical inference are based on the discrete observation of the variable x (t) "number of active cases of COVID-19 in Morocco" by using the data for the period of 28 January to 4 March 2022. Then, we analyze the mean functions by using simulated data for fit and forecast purposes. Finally, we explore the illustration of using this new process to fit and forecast the active cases of COVID-19 data. [ABSTRACT FROM AUTHOR]

This study focuses on a novel family of distributions inspired by the hyperbolic sine function. The Rayleigh distribution is the base model for the newly formed family of distributions known as the new hyperbolic Sine-Rayleigh distribution. The recommended distribution's distinct structural traits have been examined. The behaviors of the distributional functions of the proposed model are depicted in several figures. The maximum likelihood estimation procedure is employed to estimate the specified distribution parameters. A simulation study was carried out to examine and evaluate the behavior of the estimators. Moreover, the efficacy of the specified distribution is supported by realistic data sets pertaining to engineering science. [ABSTRACT FROM AUTHOR]

Studies on control charts with estimated parameters have received much attention in the recent literature. In this paper, the effect of parameter estimation on the performance of the Shewhart-type chart for the Rayleigh distribution, namely the V R chart, is first studied under the conditional perspective. It is found that parameter estimation has a serious effect on the performance of the frequentist V R chart. In order to solve this problem, the frequentist V R chart is adjusted by using the exceedance probability criterion to guarantee the in-control performance. Since the frequentist V R chart uses the sample information from Phase I, but not the process information from past experience, an alternative chart, namely the Bayesian V R chart, is proposed based on the predictive distribution of the plotting statistic. The performances of the Bayesian and adjusted frequentist V R charts are evaluated and compared in terms of the percentiles, mean, and standard deviation of the conditional average run length distribution. The results suggest that the Bayesian chart outperforms the frequentist counterpart, especially when more prior information is available. [ABSTRACT FROM AUTHOR]

The volatile and intermittent nature of renewable energy sources (RES) has a critical impact on electric power grid operations. However, there still lacks a model to price the uncertainty of renewable energy in electricity markets. This paper aims to propose a model to quantify the impact of the uncertainty of RES on the power system operating costs in an electricity market environment considering the use of flexible ramping (FR) products, compensation for wind power curtailment, and the cost for flexible load curtailment, and thus offer a method to price the uncertainty of RES. The model is based on a stochastic optimization model for power system operations considering FR products, and the uncertainty cost is calculated by comparing the dispatch cost as well as the compensation for wind power curtailment and load curtailment with and without uncertainties. The method was implemented on a modified RTS-96 test system with a high penetration of wind energy, and the uncertainty of wind power output was represented using three different distributions, namely, Gamma, Weibull, and Rayleigh. Results show that the uncertainty of wind power increases power system operating costs, and different uncertainty modeling can affect the pricing of wind power uncertainty by up to 5%. This shows that there is a need for system operators to choose the appropriate distribution to model wind power uncertainty when pricing wind power uncertainty.

Process monitoring is typically performed with quality control charts. The normality assumption is often taken into consideration for the development of control charts. However, this assumption may not hold in many real-life situations. One such circumstance is utilizing the $\mathrm {V}_{\mathrm {SQR}}$ chart to track the process variability of Rayleigh distributed processes. The structure of the $\mathrm {V}_{\mathrm {SQR}}$ chart follows the basic design of the Shewhart-type chart, which is not sensitive mainly for smaller to moderate shifts in monitoring parameter. In this paper, an enhanced approach, namely Rayleigh exponential weighted moving average (REWMA) is introduced. The suggested REWMA scheme aims to significantly improve the detection capabilities of the traditional $\mathrm {V}_{\mathrm {SQR}}$ chart. Designated limits, along with charting parameters, are evaluated for different sample sizes. The effectiveness of the suggested REWMA control chart is assessed in terms of run length distributional parameters. Moreover, the Monte Carlo simulations are made to compare the run length properties of the proposed REWMA chart with the existing competitor design. The comparative assessment demonstrates that the suggested offers a considerable enhancement relative to the competing design. An application of the REWMA chart on simulated data also reveals that the proposed chart is highly sensitive to smaller and persistent shifts in the scaling parameter of Rayleigh distribution. Finally, an example from real-life has been presented to illustrate the importance of the suggested chart.

Big data is a collection of complex and large volumes of data that is not easily handled by the traditional process. The top ten big data science communities include Kaggle, IBM data community, Reddit, open data science, data science central, data community DC, stack overflow, data quest, the data science society, and driven data. Among the online communities, Reddit is a promising online platform that connects millions of people to each other. It is a fruitful online platform that offers business firms to reach the maximum audience. In this paper, we introduce a new extended form of the generalized Rayleigh distribution to model the Reddit advertising and breast cancer data sets. The proposed model is called a new generalized Rayleigh distribution and possesses heavy-tailed properties. The maximum likelihood estimators along with certain mathematical properties are obtained. Finally, the new generalized Rayleigh distribution is applied to the Reddit advertising and breast cancer data sets and its comparisons are done with the other generalized forms of the Rayleigh distribution.

In this article, we are applying the competing risks model of product from two different lines of production. So, the comparative life test is done under type-II censoring scheme with consideration of only two independent causes of failure. The statistical analysis procedures are developed considering joint sample of production and its life distributed with the Rayleigh lifetime distribution. The point estimation and the corresponding asymptotic confidence interval of the model parameters under maximum likelihood are constructed. Two bootstrap confidence intervals, bootstrap-pp, and bootstrap-tt, are discussed. Also, Bayesian approach to estimate point and credible interval is constructed. The estimation results are discussed through data set analyses. The validity of theoretical results is assessed and compared through Monte Carlo study. Finally, some of the points are reported as a brief comment.

Color image segmentation is the primary step to elicit detailed information about the image. However, the segmentation of images under low dynamic ranges is extremely difficult. So the work has proposed an efficient color image segmentation of low-density range image using RCAB-RDMCNN enhancement technique and RBSHM segmentation algorithm. The proposed framework efficiently segments the LDR images by undergoing the following steps. Initially, the RGB formats of the LDR images are converted into HSV format. Then, the brighter as well as the darker regions from the images are segmented by using the AMOT algorithm. After that, the contrasts of the image are enhanced by using RCAB-RDMCNN. Finally, the image segmentation is performed by means of the RBSHM. The publically available LDR images are used in this research. And the results obtained by the proposed method are compared with the previous state-of-art algorithms. The experimental outcomes indicated that the proposed method segments the LDR images with the highest accuracy rate and outperforms the other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Lifetime performance indices CL is usually used as the measurement for the larger-the-better type quality characteristics to assess the process performance of products. The lifetimes of products are assumed to have Rayleigh distribution in this study. This research presents another approach to the hypothesis testing procedure for the index without the transformation of Rayleigh distribution to the exponential distribution. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample and its asymptotic distribution of this estimator is also developed to build a new hypothesis testing procedure under a pre-assigned lower specification limit. A simulation study is done and the results show that the power performance of this approach is better than the existing one. Finally, two practical examples are given to illustrate the use of two testing algorithmic procedures to determine whether the process is capable. [ABSTRACT FROM AUTHOR]

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