Pub Date : 2022-08-03DOI: 10.13052/jrss0974-8024.1527
M. Ram, Ganga Negi, Nupur Goyal, Anuj Kumar
The demand in the present global industrial system, requires the challenge to meet the growing consumer capabilities and requirements constantly. So, there is always a need to improve different parameters, one of them being different types of failures involved in the working of different engineering systems related to communication systems, manufacturing goods, nuclear and hydro power plants, automobiles and many others. Human error occurring in the working of various systems has always been the challenge to the researchers and is being constantly worked upon by the researchers in the analysis and improvement of reliability and availability of different complex and multistate systems. In the present paper, there is a three-unit system consisting of the unit A with two subunits in parallel and other units B and C are connected in series with A. The authors have investigated and analysed different reliability measures like availability, MTTF and sensitivity taking into account the human failure and carrying out rework system. This research work aims at the study of reliability and availability measures of a multi-state system incorporating human error so as to increase the efficiency of industrial systems by taking maintenance and rework measures to enhance the availability factors. This would help to understand and estimate the reliability measures of any such systems in the field of telecommunication, any electronic devices like that in small power plants, robot systems and such others. Also, a comparison has been made between the availability and reliability estimates in the presence and in the absence of human error. The techniques used are Markov process, Laplace transformation and supplementary variable technique.
{"title":"Analysis of a Stochastic Model with Rework System","authors":"M. Ram, Ganga Negi, Nupur Goyal, Anuj Kumar","doi":"10.13052/jrss0974-8024.1527","DOIUrl":"https://doi.org/10.13052/jrss0974-8024.1527","url":null,"abstract":"The demand in the present global industrial system, requires the challenge to meet the growing consumer capabilities and requirements constantly. So, there is always a need to improve different parameters, one of them being different types of failures involved in the working of different engineering systems related to communication systems, manufacturing goods, nuclear and hydro power plants, automobiles and many others. Human error occurring in the working of various systems has always been the challenge to the researchers and is being constantly worked upon by the researchers in the analysis and improvement of reliability and availability of different complex and multistate systems. In the present paper, there is a three-unit system consisting of the unit A with two subunits in parallel and other units B and C are connected in series with A. The authors have investigated and analysed different reliability measures like availability, MTTF and sensitivity taking into account the human failure and carrying out rework system. This research work aims at the study of reliability and availability measures of a multi-state system incorporating human error so as to increase the efficiency of industrial systems by taking maintenance and rework measures to enhance the availability factors. This would help to understand and estimate the reliability measures of any such systems in the field of telecommunication, any electronic devices like that in small power plants, robot systems and such others. Also, a comparison has been made between the availability and reliability estimates in the presence and in the absence of human error. The techniques used are Markov process, Laplace transformation and supplementary variable technique.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42270515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider the classical and the Bayesian inferences for unknown parameters of inverse Lomax distribution and their corresponding survival characteristics under the adaptive progressive type-II censoring scheme. In the classical setup, first we obtain the maximum likelihood estimates for the unknown shape parameter of the distribution and its corresponding survival characteristics. Further, we consider symmetric and asymmetric loss functions for the estimation of shape parameter and its corresponding survival characteristics under the Bayesian paradigm. The performances of various derived estimators were recorded using Markov chain Monte Carlo simulation technique for different sample sizes. Finally, a COVID-19 mortality data set is provided to illustrate the computation of various estimators.
{"title":"Classical and Bayesian Inference for the Inverse Lomax Distribution Under Adaptive Progressive Type-II Censored Data with COVID-19","authors":"Rashi Hora, Naresh Chandra Kabdwal, Pulkit Srivastava","doi":"10.13052/jrss0974-8024.1525","DOIUrl":"https://doi.org/10.13052/jrss0974-8024.1525","url":null,"abstract":"In this paper, we consider the classical and the Bayesian inferences for unknown parameters of inverse Lomax distribution and their corresponding survival characteristics under the adaptive progressive type-II censoring scheme. In the classical setup, first we obtain the maximum likelihood estimates for the unknown shape parameter of the distribution and its corresponding survival characteristics. Further, we consider symmetric and asymmetric loss functions for the estimation of shape parameter and its corresponding survival characteristics under the Bayesian paradigm. The performances of various derived estimators were recorded using Markov chain Monte Carlo simulation technique for different sample sizes. Finally, a COVID-19 mortality data set is provided to illustrate the computation of various estimators.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43181591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-27DOI: 10.13052/jrss0974-8024.1522
G. D’Amico, F. Gismondi, Salvatore Vergine
In this paper, the expected value of the first hitting time of a threshold of the state of charge of a battery is investigated. The model considers a battery storage system connected to a wind power plant under a ramp rate limitation scheme. The level of charge in the battery is the result of operations that are modelled by a Markov chain model with random rewards. The Markov chain and reward characteristics do depend on the considered ramp rate limitation scheme that the wind power producer has to respect in order to guarantee a quasi-stable output power to the grid. In this paper, we derive a system of integral equations for the hitting time of the state of charge of the battery and the application to real data validates the analytical results.
{"title":"A Model for the State of Charge of a Battery Connected to a Wind Power Plant Under a Ramp Rate Limitation Regime","authors":"G. D’Amico, F. Gismondi, Salvatore Vergine","doi":"10.13052/jrss0974-8024.1522","DOIUrl":"https://doi.org/10.13052/jrss0974-8024.1522","url":null,"abstract":"In this paper, the expected value of the first hitting time of a threshold of the state of charge of a battery is investigated. The model considers a battery storage system connected to a wind power plant under a ramp rate limitation scheme. The level of charge in the battery is the result of operations that are modelled by a Markov chain model with random rewards. The Markov chain and reward characteristics do depend on the considered ramp rate limitation scheme that the wind power producer has to respect in order to guarantee a quasi-stable output power to the grid. In this paper, we derive a system of integral equations for the hitting time of the state of charge of the battery and the application to real data validates the analytical results.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48525530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-27DOI: 10.13052/jrss0974-8024.1521
A. Makrides
Multi state systems can be seen as semi-Markov processes by considering an arbitrary distribution function for sojourn times. Especially, in this work, the Modified Weibull distribution is employed to be the distribution of sojourn times with a shape parameter λλ such that is member of a distributions family that is closed under minima. Parameters estimators are provided and the proposed methodology is evaluated using a detailed simulation procedure.
{"title":"Statistical Inference for Multi State Systems under the Generalized Modified Weibull Class","authors":"A. Makrides","doi":"10.13052/jrss0974-8024.1521","DOIUrl":"https://doi.org/10.13052/jrss0974-8024.1521","url":null,"abstract":"Multi state systems can be seen as semi-Markov processes by considering an arbitrary distribution function for sojourn times. Especially, in this work, the Modified Weibull distribution is employed to be the distribution of sojourn times with a shape parameter λλ such that is member of a distributions family that is closed under minima. Parameters estimators are provided and the proposed methodology is evaluated using a detailed simulation procedure.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42353850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-27DOI: 10.13052/jrss0974-8024.1524
J. E. Ruiz-Castro, Christian Acal
Two complex multi-state systems subject to multiple events are built in an algorithmic and computational way by considering phase-type distributions and Markovian arrival processes with marked arrivals. The internal performance of the system is composed of different degradation levels and internal repairable and non-repairable failures can occur. Also, the system is subject to external shocks that may provoke repairable or non-repairable failure. A multiple vacation policy is introduced in the system for the repairperson. Preventive maintenance is included in the system to improve the behaviour. Two types of task may be performed by the repairperson; corrective repair and preventive maintenance. The systems are modelled, the transient and stationary distributions are built and different performance measures are calculated in a matrix-algorithmic form. Cost and rewards are included in the model in a vector matrix way. Several economic measures are worked out and the net reward per unit of time is used to optimize the system. A numerical example shows that the system can be optimized according to the existence of preventive maintenance and the distribution of vacation time. The results have been implemented computationally with Matlab and R (packages: expm, optim).
{"title":"MMAPs to Model Complex Multi-State Systems with Vacation Policies in the Repair Facility","authors":"J. E. Ruiz-Castro, Christian Acal","doi":"10.13052/jrss0974-8024.1524","DOIUrl":"https://doi.org/10.13052/jrss0974-8024.1524","url":null,"abstract":"Two complex multi-state systems subject to multiple events are built in an algorithmic and computational way by considering phase-type distributions and Markovian arrival processes with marked arrivals. The internal performance of the system is composed of different degradation levels and internal repairable and non-repairable failures can occur. Also, the system is subject to external shocks that may provoke repairable or non-repairable failure. A multiple vacation policy is introduced in the system for the repairperson. Preventive maintenance is included in the system to improve the behaviour. Two types of task may be performed by the repairperson; corrective repair and preventive maintenance. The systems are modelled, the transient and stationary distributions are built and different performance measures are calculated in a matrix-algorithmic form. Cost and rewards are included in the model in a vector matrix way. Several economic measures are worked out and the net reward per unit of time is used to optimize the system. A numerical example shows that the system can be optimized according to the existence of preventive maintenance and the distribution of vacation time. The results have been implemented computationally with Matlab and R (packages: expm, optim).","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45050910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-27DOI: 10.13052/jrss0974-8024.1523
Md. Asraful Haque, N. Ahmad
With the increase of human dependency over computer software, considerable effort has been given to determine software reliability effectively. A huge variety of software reliability growth models (SRGMs) have been developed to explain statistically how system reliability varies over time by monitoring the failure data sets during the testing process. The paper proposes a new SRGM based on taking into account the fault removal efficiency which is the ratio of corrected and detected faults during the testing process. The new model is compared to some known model from the relevant literature for two certain data sets and it turns out to perform better in terms of four GOF benchmarks.
{"title":"A Software Reliability Model Using Fault Removal Efficiency","authors":"Md. Asraful Haque, N. Ahmad","doi":"10.13052/jrss0974-8024.1523","DOIUrl":"https://doi.org/10.13052/jrss0974-8024.1523","url":null,"abstract":"With the increase of human dependency over computer software, considerable effort has been given to determine software reliability effectively. A huge variety of software reliability growth models (SRGMs) have been developed to explain statistically how system reliability varies over time by monitoring the failure data sets during the testing process. The paper proposes a new SRGM based on taking into account the fault removal efficiency which is the ratio of corrected and detected faults during the testing process. The new model is compared to some known model from the relevant literature for two certain data sets and it turns out to perform better in terms of four GOF benchmarks.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45144503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-02DOI: 10.13052/jrss0974-8024.15114
A. James, N. Chandra, M. Pandey
The stress-strength model is a basic tool used in evaluating the reliability (R). It shows that a component or system with stress (Y) and strength (X) will fail if the stress exceeds the strength, and its counterpart allows it to function. Usually, the statistical independence between X and Y are assumed and reliability models are extensively developed in the literature. However, in real life, there are many situations in which the dependence stress-strength is taken into account. So it is important to consider and model the association between them. In this paper, we estimated R when the stress and strength parameters are linked by a Fralie-Gumble-Morgenstern copula with Lindley marginals. The estimates of reliability and dependence parameter are obtained by using maximum likelihood estimation (MLE), inference function margins (IFM), and semi parametric (SP) methods. In addition, the length of the asymptotic confidence interval and the coverage probability of the dependence parameter are also computed. A simulation study is performed to evaluate the effectiveness of the various estimates, and a real data set is also used for illustrative purposes.
{"title":"A Copula Based Stress-Strength Reliability Estimation with Lindley Marginals","authors":"A. James, N. Chandra, M. Pandey","doi":"10.13052/jrss0974-8024.15114","DOIUrl":"https://doi.org/10.13052/jrss0974-8024.15114","url":null,"abstract":"The stress-strength model is a basic tool used in evaluating the reliability (R). It shows that a component or system with stress (Y) and strength (X) will fail if the stress exceeds the strength, and its counterpart allows it to function. Usually, the statistical independence between X and Y are assumed and reliability models are extensively developed in the literature. However, in real life, there are many situations in which the dependence stress-strength is taken into account. So it is important to consider and model the association between them. In this paper, we estimated R when the stress and strength parameters are linked by a Fralie-Gumble-Morgenstern copula with Lindley marginals. The estimates of reliability and dependence parameter are obtained by using maximum likelihood estimation (MLE), inference function margins (IFM), and semi parametric (SP) methods. In addition, the length of the asymptotic confidence interval and the coverage probability of the dependence parameter are also computed. A simulation study is performed to evaluate the effectiveness of the various estimates, and a real data set is also used for illustrative purposes.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48094176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-02DOI: 10.13052/jrss0974-8024.15115
Vibha Trivedi, Krishan Kumar Pandey, A. Trivedi
Sharing of Do-It-Yourself (DIY) cooking outcomes on various social media platforms was one of the most visible phenomena on the digital landscapes during COVID-19 led lockdowns. Since the prosumption of food is not considered as a source of alternative food system only, but also as a source of pleasure, DIY-cooking-related social media posts during the lockdown were prevalent among internet users. This paper examines variations in the social media posting behavior of food prosumers based on four individual and three social factors of gender, age, marital status, and family structure. Responses from 198 Facebook food community members were used to test the statistical hypotheses. The analyses report that the need for entertainment value while posting on social media was different among different demographic factors, whereas self-discovery and social enhancement did not exhibit variations across demographics. The need for social presence mattered more for unmarried people during social isolation whereas females used DIY-cooking posting to fulfil the need for uniqueness. The implications for social sustainability and business practices are also discussed.
{"title":"Prosumption for Social Sustainability: Social-media Posting of DIY-cooking Outcomes During COVID-19","authors":"Vibha Trivedi, Krishan Kumar Pandey, A. Trivedi","doi":"10.13052/jrss0974-8024.15115","DOIUrl":"https://doi.org/10.13052/jrss0974-8024.15115","url":null,"abstract":"Sharing of Do-It-Yourself (DIY) cooking outcomes on various social media platforms was one of the most visible phenomena on the digital landscapes during COVID-19 led lockdowns. Since the prosumption of food is not considered as a source of alternative food system only, but also as a source of pleasure, DIY-cooking-related social media posts during the lockdown were prevalent among internet users. This paper examines variations in the social media posting behavior of food prosumers based on four individual and three social factors of gender, age, marital status, and family structure. Responses from 198 Facebook food community members were used to test the statistical hypotheses. The analyses report that the need for entertainment value while posting on social media was different among different demographic factors, whereas self-discovery and social enhancement did not exhibit variations across demographics. The need for social presence mattered more for unmarried people during social isolation whereas females used DIY-cooking posting to fulfil the need for uniqueness. The implications for social sustainability and business practices are also discussed.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46220298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-07DOI: 10.13052/jrss0974-8024.15113
Priyanka Chhaparwal, Sanjay Kumar
Statisticians often use auxiliary information at an estimation stage to increase efficiencies of estimators. In this article, we suggest modified ratio- and product-type estimators utilizing the known value of the coefficient of variation of the auxiliary variable for a time-based survey. Further, to excel the performance of the suggested estimators, we utilize information from the past surveys along with the current surveys through hybrid exponentially weighted average. We obtain expressions for biases and mean square errors of the suggested estimators. The conditions, under which the suggested estimators have less mean square errors than that of other existing estimators, are also obtained. The results obtained through an empirical analysis examine the use of information from past surveys along with current surveys and show that the mean square errors and biases of the suggested estimators are less than that of the existing estimators. For example: for a sample size 5, mean square error and bias of the suggested ratio-type estimator are (0.0414,0.0065) which are less than (0.5581,0.0944) of the existing Cochran (1940) estimator, (0.4788,0.0758), of Sisodia and Dwivedi (1981) estimator and (0.0482,0.0082) of Muhammad Noor-ul-Amin (2020) estimator. Similarly, mean square error and bias of the suggested product- type estimator are (0.0025,−0.0006) which are less than (0.0612,−0.0096) of the existing Murthy (1964) estimator, (0.0286,−0.0071), of Pandey and Dubey (1988) estimator and (0.0053,−0.0008) of Muhammad Noor-ul-Amin (2020) estimator.
统计学家经常在估计阶段使用辅助信息来提高估计的效率。在这篇文章中，我们建议使用辅助变量变异系数的已知值对基于时间的调查进行修正的比率和乘积类型估计。此外，为了提高建议估计量的性能，我们通过混合指数加权平均值利用了过去调查和当前调查的信息。我们得到了所建议的估计量的偏差和均方误差的表达式。还得到了所提出的估计量的均方误差小于其他现有估计量的条件。通过实证分析获得的结果检验了过去调查和当前调查中信息的使用情况，并表明所建议的估计量的均方误差和偏差小于现有估计量。例如：对于样本量为5的情况，所建议的比率型估计器的均方误差和偏差为（0.0414,0.0065），小于现有的Cochran（1940）估计器（0.5581,0.0944）、Sisodia和Dwivedi（1981）估计量（0.4788,0.0758）和Muhammad Noor ul Amin（2020）估计量的（0.0482,0.0082）。类似地，所提出的乘积型估计器的均方误差和偏差为（0.0025，−0.0006），小于现有Murthy（1964）估计器（0.0612，−0.0096）、Pandey和Dubey（1988）估计量（0.0286，−0.0071）和Muhammad Noor ul Amin（2020）估计量的（0.0053，−0.0008）。
{"title":"Improving Efficiencies of Ratio- and Product-type Estimators for Estimating Population Mean for Time-based Survey","authors":"Priyanka Chhaparwal, Sanjay Kumar","doi":"10.13052/jrss0974-8024.15113","DOIUrl":"https://doi.org/10.13052/jrss0974-8024.15113","url":null,"abstract":"Statisticians often use auxiliary information at an estimation stage to increase efficiencies of estimators. In this article, we suggest modified ratio- and product-type estimators utilizing the known value of the coefficient of variation of the auxiliary variable for a time-based survey. Further, to excel the performance of the suggested estimators, we utilize information from the past surveys along with the current surveys through hybrid exponentially weighted average. We obtain expressions for biases and mean square errors of the suggested estimators. The conditions, under which the suggested estimators have less mean square errors than that of other existing estimators, are also obtained. The results obtained through an empirical analysis examine the use of information from past surveys along with current surveys and show that the mean square errors and biases of the suggested estimators are less than that of the existing estimators. For example: for a sample size 5, mean square error and bias of the suggested ratio-type estimator are (0.0414,0.0065) which are less than (0.5581,0.0944) of the existing Cochran (1940) estimator, (0.4788,0.0758), of Sisodia and Dwivedi (1981) estimator and (0.0482,0.0082) of Muhammad Noor-ul-Amin (2020) estimator. Similarly, mean square error and bias of the suggested product- type estimator are (0.0025,−0.0006) which are less than (0.0612,−0.0096) of the existing Murthy (1964) estimator, (0.0286,−0.0071), of Pandey and Dubey (1988) estimator and (0.0053,−0.0008) of Muhammad Noor-ul-Amin (2020) estimator.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49401758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-07DOI: 10.13052/jrss0974-8024.15112
A. Kaushik, U. Nigam
In this paper, we propose an extension to the Topp-Leone distribution, as introduced by [20] using the Generalized-DUS transformation given by [8]. The Topp-Leone distribution is defined on interval (0,1) and has a characteristic J-shaped frequency curve. The newly extended version of Topp-Leone distribution accommodates a variety of shapes of hazard rate functions making it a versatile distribution. We have also derived explicit expressions for some properties like ordinary moments, conditional moments, distribution of order statistics, quantiles, mean deviation, and entropy. Further, we have also discussed results on identifiability, stress-strength reliability, and stochastic ordering that are concerned with two independent random variables. For inference regarding the unknown parameters of the distribution, we derive the equations which give their maximum likelihood estimators. We also present the asymptotic confidence intervals of the unknown parameters of the distribution, based on large sample property, using the Fisher information matrix. To facilitate further studies, a step-by-step algorithm is presented to produce a random sample from the distribution. Further, extensive simulation experiments are done to study the long-term behavior of the maximum likelihood estimators of the parameters through their mean squared error and mean absolute bias on the basis of large number of samples. The consistency of the MLEs is empirically proved. Lastly, the application of the proposed distribution is shown by fitting a real-life dataset over some existing distributions in the same range.
{"title":"GDUS-Modified Topp-Leone Distribution: A New Distribution with Increasing, Decreasing, and Bathtub Hazard Functions","authors":"A. Kaushik, U. Nigam","doi":"10.13052/jrss0974-8024.15112","DOIUrl":"https://doi.org/10.13052/jrss0974-8024.15112","url":null,"abstract":"In this paper, we propose an extension to the Topp-Leone distribution, as introduced by [20] using the Generalized-DUS transformation given by [8]. The Topp-Leone distribution is defined on interval (0,1) and has a characteristic J-shaped frequency curve. The newly extended version of Topp-Leone distribution accommodates a variety of shapes of hazard rate functions making it a versatile distribution. We have also derived explicit expressions for some properties like ordinary moments, conditional moments, distribution of order statistics, quantiles, mean deviation, and entropy. Further, we have also discussed results on identifiability, stress-strength reliability, and stochastic ordering that are concerned with two independent random variables. For inference regarding the unknown parameters of the distribution, we derive the equations which give their maximum likelihood estimators. We also present the asymptotic confidence intervals of the unknown parameters of the distribution, based on large sample property, using the Fisher information matrix. To facilitate further studies, a step-by-step algorithm is presented to produce a random sample from the distribution. Further, extensive simulation experiments are done to study the long-term behavior of the maximum likelihood estimators of the parameters through their mean squared error and mean absolute bias on the basis of large number of samples. The consistency of the MLEs is empirically proved. Lastly, the application of the proposed distribution is shown by fitting a real-life dataset over some existing distributions in the same range.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42752644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：