The concept of generalized order statistics has been introduced as a unified approach to a variety of models of ordered random variables with different interpretations. In this paper, we develop methodology for constr...The concept of generalized order statistics has been introduced as a unified approach to a variety of models of ordered random variables with different interpretations. In this paper, we develop methodology for constructing inference based on n selected generalized order statistics (GOS) from inverse Weibull distribution (IWD), Bayesian and non-Bayesian approaches have been used to obtain the estimators of the parameters and reliability function. We have examined Bayes estimates under various losses such as the balanced squared error (balanced SEL) and balanced LINEX loss functions are considered. We show that Bayes estimate under balanced SEL and balanced LINEX loss functions are more general, which include the symmetric and asymmetric losses as special cases. This was done under assumption of discrete-continuous mixture prior for the unknown model parameters. The parametric bootstrap method has been used to construct confidence interval for the parameters and reliability function. Progressively type-II censored and k-record values as a special case of GOS are considered. Finally a practical example using real data set was used for illustration.展开更多
<span style="font-family:Verdana;">In this paper, we derived a new distribution named as truncated Weibull Rayleigh (TW-R) distribution. Its characterization and statistical properties are obtained, su...<span style="font-family:Verdana;">In this paper, we derived a new distribution named as truncated Weibull Rayleigh (TW-R) distribution. Its characterization and statistical properties are obtained, such as reliability function, hazard function, reversed</span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">hazard rate function, cumulative hazard rate function, quantile function, rth moment, incomplete moments, Rényi and q entropies and order statistic. Parameter estimation is implemented using method of maximum-likelihood estimation and Fisher information matrix is derived. Finally, application of the presented new distribution to a real data representing the failure times of 63 airbcraft</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Windshield is given and its goodness-of-fit is demonstrated. In addition to, comparisons to other models are implemented to show the flexibility of the presented</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">model.</span></span></span>展开更多
In recent years,there has been an increased interest among the researchers to propose new families of distributions to provide the best fit to lifetime data with monotonic(increasing,decreasing,constant)and non-monoto...In recent years,there has been an increased interest among the researchers to propose new families of distributions to provide the best fit to lifetime data with monotonic(increasing,decreasing,constant)and non-monotonic(unimodal,modified unimodal,bathtub)hazard functions.We further carry this area of research and propose a new family of lifetime distributions called a new logarithmic family via the T-X family approach.For the proposed family,explicit expressions for some mathematical properties along with the estimation of parameters through Maximum likelihood method are discussed.A sub-model,called a new logarithmic Weibull distribution is taken up.The proposed model is very flexible and can be used to model data with increasing,decreasing,modified unimodal or bathtub shaped hazard rates.The maximum likelihood estimators of the model parameters are obtained.To assess the behavior of the maximum likelihood estimators,a comprehensive Monte Carlo simulation study has been carried out.Finally,the potentiality of the new model is shown via analyzing two real data sets taken from reliability engineering and biomedical fields.The comparison of the proposed model is made with the other well-known competitors such as(i)the three parameters exponentiated Weibull and Marshall–Olkin Weibull distributions and(ii)a four-parameter beta Weibull distribution.The practical applications show that the proposed model performs much better than the competitive models and can be used as a good candidate model to analyze data in engineering,medical sciences and other related fields.展开更多
When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are func...When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .展开更多
When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are func...When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .展开更多
文摘The concept of generalized order statistics has been introduced as a unified approach to a variety of models of ordered random variables with different interpretations. In this paper, we develop methodology for constructing inference based on n selected generalized order statistics (GOS) from inverse Weibull distribution (IWD), Bayesian and non-Bayesian approaches have been used to obtain the estimators of the parameters and reliability function. We have examined Bayes estimates under various losses such as the balanced squared error (balanced SEL) and balanced LINEX loss functions are considered. We show that Bayes estimate under balanced SEL and balanced LINEX loss functions are more general, which include the symmetric and asymmetric losses as special cases. This was done under assumption of discrete-continuous mixture prior for the unknown model parameters. The parametric bootstrap method has been used to construct confidence interval for the parameters and reliability function. Progressively type-II censored and k-record values as a special case of GOS are considered. Finally a practical example using real data set was used for illustration.
文摘<span style="font-family:Verdana;">In this paper, we derived a new distribution named as truncated Weibull Rayleigh (TW-R) distribution. Its characterization and statistical properties are obtained, such as reliability function, hazard function, reversed</span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">hazard rate function, cumulative hazard rate function, quantile function, rth moment, incomplete moments, Rényi and q entropies and order statistic. Parameter estimation is implemented using method of maximum-likelihood estimation and Fisher information matrix is derived. Finally, application of the presented new distribution to a real data representing the failure times of 63 airbcraft</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Windshield is given and its goodness-of-fit is demonstrated. In addition to, comparisons to other models are implemented to show the flexibility of the presented</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">model.</span></span></span>
基金The first and second authors acknowledge the Research on the Demand Side and Supply Side Demand Mechanism of Overcapacity Capacity of China's Machinery Manufacturing Industryin the“One Belt and One Road”Strategy,16BJY079.
文摘In recent years,there has been an increased interest among the researchers to propose new families of distributions to provide the best fit to lifetime data with monotonic(increasing,decreasing,constant)and non-monotonic(unimodal,modified unimodal,bathtub)hazard functions.We further carry this area of research and propose a new family of lifetime distributions called a new logarithmic family via the T-X family approach.For the proposed family,explicit expressions for some mathematical properties along with the estimation of parameters through Maximum likelihood method are discussed.A sub-model,called a new logarithmic Weibull distribution is taken up.The proposed model is very flexible and can be used to model data with increasing,decreasing,modified unimodal or bathtub shaped hazard rates.The maximum likelihood estimators of the model parameters are obtained.To assess the behavior of the maximum likelihood estimators,a comprehensive Monte Carlo simulation study has been carried out.Finally,the potentiality of the new model is shown via analyzing two real data sets taken from reliability engineering and biomedical fields.The comparison of the proposed model is made with the other well-known competitors such as(i)the three parameters exponentiated Weibull and Marshall–Olkin Weibull distributions and(ii)a four-parameter beta Weibull distribution.The practical applications show that the proposed model performs much better than the competitive models and can be used as a good candidate model to analyze data in engineering,medical sciences and other related fields.
文摘When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .
文摘When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .
