Pub Date : 2021-10-26DOI: 10.6092/ISSN.1973-2201/12309
H. Rehman, N. Chandra
In this paper we deal with the modelling of cumulative incidence function using improper Gompertz distribution based on middle censored competing risks survival data. Together with the unknown parameters, cumulative incidence function also estimated. In classical set up, we derive the point estimates using maximum likelihood estimator and midpoint approximation methods. The asymptotic confidence interval are obtained based on asymptotic normality properties of maximum likelihood estimator. We also derive the Bayes estimates with associated credible intervals based on informative and non-informative types of priors under two loss functions such as squared error and LINEX loss functions. A simulation study is conducted for comprehensive comparison between various estimators proposed in this paper. A real life data set is also used for illustration.
{"title":"Estimation of Cumulative Incidence Function in the Presence of Middle Censoring Using Improper Gompertz Distribution","authors":"H. Rehman, N. Chandra","doi":"10.6092/ISSN.1973-2201/12309","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/12309","url":null,"abstract":"In this paper we deal with the modelling of cumulative incidence function using improper Gompertz distribution based on middle censored competing risks survival data. Together with the unknown parameters, cumulative incidence function also estimated. In classical set up, we derive the point estimates using maximum likelihood estimator and midpoint approximation methods. The asymptotic confidence interval are obtained based on asymptotic normality properties of maximum likelihood estimator. We also derive the Bayes estimates with associated credible intervals based on informative and non-informative types of priors under two loss functions such as squared error and LINEX loss functions. A simulation study is conducted for comprehensive comparison between various estimators proposed in this paper. A real life data set is also used for illustration.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"81 1","pages":"163-182"},"PeriodicalIF":1.9,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48154934","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 : 2021-10-26DOI: 10.6092/ISSN.1973-2201/12090
S. Ando
This study proposes a polynomial columns-parameter symmetry model for square contingency tables with the same row and column ordinal classifications. In the proposed model, the odds for all i < j that an observation will fall in row category i and column category j instead of row category j and column category i depend on only the value of column category j . The proposed model is original because many asymmetry models in square contingency tables depend on the both values of row and column category. The proposed model constantly holds when the columns-parameter symmetry model holds; but the converse does not necessarily hold. This study shows that it is necessary to satisfy the polynomial columns-marginal symmetry model, in addition to the columns-parameter symmetry model, to satisfy the proposed model. This decomposition theorem is useful for explaining why the proposed model does not hold. Moreover, this study shows the value of likelihood ratio chi-square statistic for testing the proposed model is equal to the sum of that for testing the decomposed two models.
{"title":"Polynomial Columns-Parameter Symmetry Model and its Decomposition for Square Contingency Tables","authors":"S. Ando","doi":"10.6092/ISSN.1973-2201/12090","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/12090","url":null,"abstract":"This study proposes a polynomial columns-parameter symmetry model for square contingency tables with the same row and column ordinal classifications. In the proposed model, the odds for all i < j that an observation will fall in row category i and column category j instead of row category j and column category i depend on only the value of column category j . The proposed model is original because many asymmetry models in square contingency tables depend on the both values of row and column category. The proposed model constantly holds when the columns-parameter symmetry model holds; but the converse does not necessarily hold. This study shows that it is necessary to satisfy the polynomial columns-marginal symmetry model, in addition to the columns-parameter symmetry model, to satisfy the proposed model. This decomposition theorem is useful for explaining why the proposed model does not hold. Moreover, this study shows the value of likelihood ratio chi-square statistic for testing the proposed model is equal to the sum of that for testing the decomposed two models.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"81 1","pages":"123-134"},"PeriodicalIF":1.9,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44026585","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 : 2021-10-26DOI: 10.6092/ISSN.1973-2201/10993
J. T. Eghwerido, Joel Oruaoghene Ogbo, Adebola Evelyn Omotoye
This article introduces three parameters class for lifetime Poisson processes in the Marshall-Olkin transformation family that are increasing, bathtub and skewed. Some structural mathematical properties of the Marshall-Olkin Gompertz (MO-G) model were derived. The MO-G model parameters were established by maximum likelihood approach. The flexibility, efficiency, and behavior of the MO-G model estimators were examined through simulation. The empirical applicability, flexibility and proficiency of the MO-G model was scrutinized by a real-life dataset. The proposed MO-G model provides a better fit when compared to existing models in statistical literature and can serve as an alternative model to those appearing in modeling Poisson processes.
{"title":"The Marshall-Olkin Gompertz Distribution: Properties and Applications","authors":"J. T. Eghwerido, Joel Oruaoghene Ogbo, Adebola Evelyn Omotoye","doi":"10.6092/ISSN.1973-2201/10993","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/10993","url":null,"abstract":"This article introduces three parameters class for lifetime Poisson processes in the Marshall-Olkin transformation family that are increasing, bathtub and skewed. Some structural mathematical properties of the Marshall-Olkin Gompertz (MO-G) model were derived. The MO-G model parameters were established by maximum likelihood approach. The flexibility, efficiency, and behavior of the MO-G model estimators were examined through simulation. The empirical applicability, flexibility and proficiency of the MO-G model was scrutinized by a real-life dataset. The proposed MO-G model provides a better fit when compared to existing models in statistical literature and can serve as an alternative model to those appearing in modeling Poisson processes.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"81 1","pages":"183-215"},"PeriodicalIF":1.9,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47704331","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 : 2021-10-26DOI: 10.6092/ISSN.1973-2201/12336
Kamala Naganathan Radhalakshmi, M. L. William
In a good number of real life situations, the observations on a random variable of interest tend to concentrate either too closely or too thinly around a central point but symmetrically like the normal distribution. The symmetric structure of the density function appears like that of a normal distribution but the concentration of the observations can be either thicker or thinner around the mean. This paper attempts to generate a family of densities that are symmetric like normal butwith different kurtosis. Drawing inspiration from a recent work on multivariate leptokurtic normal distribution, this paper seeks to consider the univariate case and adopt a different approach to generate a family to be called ’univariate non-mesokurtic normal’ family.The symmetricity of the densities is brought out by a uniform random variable while the kurtosis variation is brought about by a chi generator. Some of the properties of the resulting class of distributions and the pameter estimation are discussed.
{"title":"A Class of Univariate Non-Mesokurtic Distributions Using a Continuous Uniform Symmetrizer and Chi Generator","authors":"Kamala Naganathan Radhalakshmi, M. L. William","doi":"10.6092/ISSN.1973-2201/12336","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/12336","url":null,"abstract":"In a good number of real life situations, the observations on a random variable of interest tend to concentrate either too closely or too thinly around a central point but symmetrically like the normal distribution. The symmetric structure of the density function appears like that of a normal distribution but the concentration of the observations can be either thicker or thinner around the mean. This paper attempts to generate a family of densities that are symmetric like normal butwith different kurtosis. Drawing inspiration from a recent work on multivariate leptokurtic normal distribution, this paper seeks to consider the univariate case and adopt a different approach to generate a family to be called ’univariate non-mesokurtic normal’ family.The symmetricity of the densities is brought out by a uniform random variable while the kurtosis variation is brought about by a chi generator. Some of the properties of the resulting class of distributions and the pameter estimation are discussed.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"81 1","pages":"217-227"},"PeriodicalIF":1.9,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45353938","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 : 2021-10-26DOI: 10.6092/ISSN.1973-2201/11635
H. Yousof, C. Chesneau, G. Hamedani, M. Ibrahim
In this work, a new discrete distribution which includes the discrete Burr-Hatke distribution is defined and studied. Relevant statistical properties are derived. The probability mass function of the new distribution can be "right skewed" with different shapes, bimodal and "uniformed". Also, the corresponding hazard rate function can be "monotonically decreasing", "upside down", "monotonically increasing", "upside down increasing", and "upside down-constant-increasing". A numerical analysis for the mean, variance, skewness, kurtosis and the index of dispersion is presented. The new distribution could be useful in the modeling of "under-dispersed" or "overdispersed" count data. Certain characterizations of the new distribution are presented. These characterizations are based on the conditional expectation of a certain function of the random variable and in terms of the hazard rate function. Bayesian and non-Bayesian estimation methods are considered. Numerical simulations for comparing Bayesian and non-Bayesian estimation methods are performed. The new model is applied for modeling carious teeth data and counts of cysts of kidneys data.
{"title":"A New Discrete Distribution: Properties, Characterizations, Modeling Real Count Data, Bayesian and Non-Bayesian Estimations","authors":"H. Yousof, C. Chesneau, G. Hamedani, M. Ibrahim","doi":"10.6092/ISSN.1973-2201/11635","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/11635","url":null,"abstract":"In this work, a new discrete distribution which includes the discrete Burr-Hatke distribution is defined and studied. Relevant statistical properties are derived. The probability mass function of the new distribution can be \"right skewed\" with different shapes, bimodal and \"uniformed\". Also, the corresponding hazard rate function can be \"monotonically decreasing\", \"upside down\", \"monotonically increasing\", \"upside down increasing\", and \"upside down-constant-increasing\". A numerical analysis for the mean, variance, skewness, kurtosis and the index of dispersion is presented. The new distribution could be useful in the modeling of \"under-dispersed\" or \"overdispersed\" count data. Certain characterizations of the new distribution are presented. These characterizations are based on the conditional expectation of a certain function of the random variable and in terms of the hazard rate function. Bayesian and non-Bayesian estimation methods are considered. Numerical simulations for comparing Bayesian and non-Bayesian estimation methods are performed. The new model is applied for modeling carious teeth data and counts of cysts of kidneys data.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"81 1","pages":"135-162"},"PeriodicalIF":1.9,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41761097","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 : 2021-09-03DOI: 10.6092/ISSN.1973-2201/11101
M. Irshad, Veena D’cruz, R. Maya
The Lindley distribution was proposed in the context of Bayesian statistics as a counter example of fiducial statistics. In this paper, we propose Zografos Balakrishnan Lindley (ZBL) distribution in which Lindley distribution is a special case. Some properties of the new distribution is obtained such as moments, hazard rate function, reliability function etc. The parameters are estimated using the method of maximum likelihood. Finally an application of the proposed distribution to a real data set is illustrated and it is concluded that Zogarfos Balakrishnan Lindley (ZBL) distribution provides better fit than other classical distributions.
{"title":"The Zografos-Balakrishnan Lindley Distribution: Properties and Applications","authors":"M. Irshad, Veena D’cruz, R. Maya","doi":"10.6092/ISSN.1973-2201/11101","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/11101","url":null,"abstract":"The Lindley distribution was proposed in the context of Bayesian statistics as a counter example of fiducial statistics. In this paper, we propose Zografos Balakrishnan Lindley (ZBL) distribution in which Lindley distribution is a special case. Some properties of the new distribution is obtained such as moments, hazard rate function, reliability function etc. The parameters are estimated using the method of maximum likelihood. Finally an application of the proposed distribution to a real data set is illustrated and it is concluded that Zogarfos Balakrishnan Lindley (ZBL) distribution provides better fit than other classical distributions.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"81 1","pages":"45-64"},"PeriodicalIF":1.9,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43417314","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 : 2021-09-03DOI: 10.6092/ISSN.1973-2201/12433
D. Karagöz, N. A. Tutkun
The aim of this study is to estimate the robust survival function for the Weibull distribution. Since the survival function of Weibull distribution is based on the parameters, we consider two robust and explicit Weibull parameter estimators proposed by Boudt et al. (2011). The quantile and the quantile least squares which are all robust to censored data is used as an alternative to the maximum likelihood estimation of the Weibull parameters. The proposed estimators are applied to Hodgin’s disease data which produces smaller variances for the robust survival function. The advantage of new methods is that they are numerically explicit in applications. Monte Carlo simulation is performed to compare the behaviours of the proposed robust estimators in the presence of right, left and interval censored observations considering different censoring rates. The simulation results show that the proposed robust estimators are better than the maximum likelihood estimator.
本研究的目的是估计威布尔分布的鲁棒生存函数。由于威布尔分布的生存函数是基于参数的，我们考虑了Boudt et al.(2011)提出的两个鲁棒和显式威布尔参数估计器。分位数和分位数最小二乘对截尾数据都具有鲁棒性，可用来替代威布尔参数的极大似然估计。所提出的估计量应用于霍奇金病数据，该数据对鲁棒生存函数产生较小的方差。新方法的优点是它们在应用程序中是数字显式的。通过蒙特卡罗仿真比较了所提出的鲁棒估计器在考虑不同审查率的右、左和区间审查观测值存在下的行为。仿真结果表明，所提出的鲁棒估计量优于极大似然估计量。
{"title":"Robust Estimations of Survival Function for Weibull Distribution","authors":"D. Karagöz, N. A. Tutkun","doi":"10.6092/ISSN.1973-2201/12433","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/12433","url":null,"abstract":"The aim of this study is to estimate the robust survival function for the Weibull distribution. Since the survival function of Weibull distribution is based on the parameters, we consider two robust and explicit Weibull parameter estimators proposed by Boudt et al. (2011). The quantile and the quantile least squares which are all robust to censored data is used as an alternative to the maximum likelihood estimation of the Weibull parameters. The proposed estimators are applied to Hodgin’s disease data which produces smaller variances for the robust survival function. The advantage of new methods is that they are numerically explicit in applications. Monte Carlo simulation is performed to compare the behaviours of the proposed robust estimators in the presence of right, left and interval censored observations considering different censoring rates. The simulation results show that the proposed robust estimators are better than the maximum likelihood estimator.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"81 1","pages":"3-23"},"PeriodicalIF":1.9,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45711778","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 : 2021-09-03DOI: 10.6092/ISSN.1973-2201/9432
M. Irshad, R. Maya, Sasikumar Arun
In this work, we have considered a lifetime distribution namely Muth distribution and pointed out instances where it appears as a good model to study the stochastic nature of the variable under consideration. We have derived the best linear unbiased estimator (BLUE) of the scale parameter of the Muth distribution based on order statistics for some known values of the shape parameter.We have further estimated the scale parameter of Muth distribution by U-statistics based on best linear functions of order statistics as kernels. The efficiency of the BLUE relative to the usual unbiased estimator has been also evaluated. An illustration describing the performance of U-statistics estimation method when compared with the classical maximum likelihood method is also given.
{"title":"Muth Distribution and Estimation of a Parameter Using Order Statistics","authors":"M. Irshad, R. Maya, Sasikumar Arun","doi":"10.6092/ISSN.1973-2201/9432","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/9432","url":null,"abstract":"In this work, we have considered a lifetime distribution namely Muth distribution and pointed out instances where it appears as a good model to study the stochastic nature of the variable under consideration. We have derived the best linear unbiased estimator (BLUE) of the scale parameter of the Muth distribution based on order statistics for some known values of the shape parameter.We have further estimated the scale parameter of Muth distribution by U-statistics based on best linear functions of order statistics as kernels. The efficiency of the BLUE relative to the usual unbiased estimator has been also evaluated. An illustration describing the performance of U-statistics estimation method when compared with the classical maximum likelihood method is also given.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"81 1","pages":"93-119"},"PeriodicalIF":1.9,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41827213","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 : 2021-09-03DOI: 10.6092/ISSN.1973-2201/10718
Haseeb Athar, Y. Abdel-Aty, M. A. Ali
In this paper characterization properties based on conditional expectation of a continuous function of random variable are studied when truncation is from both the sides, left and right. Then, these results are applied to obtain the k-th doubly truncated moment for a general class of distribution. Further, some examples and particular cases based on this general class of distributions are also demonstrated. The results are obtained in simple and explicit manner which also unifies the earlier results obtained by several authors. In the end, simulation study is performed to validate the correctness of theoretical characterization results and then two real life data sets are used to demonstrate the applications of these results.
{"title":"Characterization of Generalized Distribution by Doubly Truncated Moment","authors":"Haseeb Athar, Y. Abdel-Aty, M. A. Ali","doi":"10.6092/ISSN.1973-2201/10718","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/10718","url":null,"abstract":"In this paper characterization properties based on conditional expectation of a continuous function of random variable are studied when truncation is from both the sides, left and right. Then, these results are applied to obtain the k-th doubly truncated moment for a general class of distribution. Further, some examples and particular cases based on this general class of distributions are also demonstrated. The results are obtained in simple and explicit manner which also unifies the earlier results obtained by several authors. In the end, simulation study is performed to validate the correctness of theoretical characterization results and then two real life data sets are used to demonstrate the applications of these results.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"81 1","pages":"25-44"},"PeriodicalIF":1.9,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45107827","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 : 2021-09-03DOI: 10.6092/ISSN.1973-2201/10025
N. Choudhary, Abhishek Tyagi, B. Singh
In this study, we introduce an extended version of the modified Weibull distribution with an additional shape parameter, in order to provide more flexibility to its density and the hazard rate function. The distribution is capable of modeling the bathtub-shaped, decreasing, increasing and the constant hazard rate function. The proposed model contains sub-models that are widely used in lifetime data analysis such as the modified Weibull, Chen, extreme value, Weibull, Rayleigh, and exponential distributions. We study its statistical properties which include the hazard rate function, moments and distribution of the order statistics. The parameters involved in the model are estimated by using maximum likelihood and the Bayesian method of estimation. In Bayesian estimation, we assume independent Gamma priors for the parameters and MCMC technique such as the Metropolis-Hastings algorithm within Gibbs sampler has been implemented to obtain the sample-based estimators and the highest posterior density intervals of the parameters. Tierney and Kadane (1986) approximation is also used to obtain Bayes estimators of the parameters. In order to highlight the relative importance of various estimates obtained, a simulation study is carried out. The usefulness of the proposed model is illustrated using two real datasets.
在本研究中，我们引入了一个带有额外形状参数的修正威布尔分布的扩展版本，以便为其密度和危险率函数提供更大的灵活性。该分布能够模拟出浴缸型、递减型、递增型和恒定型的危险率函数。该模型包含了在生命周期数据分析中广泛使用的子模型，如修正Weibull、Chen、极值、Weibull、Rayleigh和指数分布。我们研究了它的统计性质，包括危险率函数、矩和阶统计量的分布。采用极大似然法和贝叶斯估计法对模型中涉及的参数进行估计。在贝叶斯估计中，我们假设参数具有独立的Gamma先验，并采用Gibbs采样器中的Metropolis-Hastings算法等MCMC技术来获得基于样本的估计量和参数的最高后验密度区间。Tierney and Kadane(1986)近似也用于获得参数的贝叶斯估计。为了突出所获得的各种估计的相对重要性，进行了模拟研究。用两个实际数据集说明了该模型的有效性。
{"title":"A Flexible Bathtub-Shaped Failure Time Model: Properties and Associated Inference","authors":"N. Choudhary, Abhishek Tyagi, B. Singh","doi":"10.6092/ISSN.1973-2201/10025","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/10025","url":null,"abstract":"In this study, we introduce an extended version of the modified Weibull distribution with an additional shape parameter, in order to provide more flexibility to its density and the hazard rate function. The distribution is capable of modeling the bathtub-shaped, decreasing, increasing and the constant hazard rate function. The proposed model contains sub-models that are widely used in lifetime data analysis such as the modified Weibull, Chen, extreme value, Weibull, Rayleigh, and exponential distributions. We study its statistical properties which include the hazard rate function, moments and distribution of the order statistics. The parameters involved in the model are estimated by using maximum likelihood and the Bayesian method of estimation. In Bayesian estimation, we assume independent Gamma priors for the parameters and MCMC technique such as the Metropolis-Hastings algorithm within Gibbs sampler has been implemented to obtain the sample-based estimators and the highest posterior density intervals of the parameters. Tierney and Kadane (1986) approximation is also used to obtain Bayes estimators of the parameters. In order to highlight the relative importance of various estimates obtained, a simulation study is carried out. The usefulness of the proposed model is illustrated using two real datasets.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":"81 1","pages":"65-92"},"PeriodicalIF":1.9,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49010290","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}
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