In this paper, we derive the distributions of concomitants of record values from generalized Farlie-Gumbel-Morgenstern family of bivariate distributions. We derive the single and the product moments of the concomitant...In this paper, we derive the distributions of concomitants of record values from generalized Farlie-Gumbel-Morgenstern family of bivariate distributions. We derive the single and the product moments of the concomitants for the general case. The results are then applied to the ease of the two-parameter exponential marginal distributions. Using concomitants of record values we derive the best linear unbiased estimators of parameters of the marginal distributions. Moreover, two methods for obtaining predictors of concomitants of record values are presented. Finally, a numerical illustration is performed to highlight the theoretical results obtained.展开更多
The power generalized Weibull distribution has been proposed recently by[24]as an alternative to the gamma,Weibull and the exponentiated Weibull distributions.The power generalized Weibull family is suitable for model...The power generalized Weibull distribution has been proposed recently by[24]as an alternative to the gamma,Weibull and the exponentiated Weibull distributions.The power generalized Weibull family is suitable for modeling data that indicate nonmonotone hazard rates and can be used in survival analysis and reliability studies.Usefulness andflexibility of the family are illustrated by reanalyzing Efron’s data pertaining to a head-and-neck cancer clinical trial.These data involve censoring and indicate unimodal hazard rate.For this distribution,some recurrence relations are established for the single and product moments of upper record values.Further,using these relations,we have obtained means,variances and covariances of upper record values from samples of sizes up to 10 for various values of the parameters and present them infigures.Real data set is analyzed to illustrate theflexibility and importance of the model.展开更多
Based on lower record values,we first derive the exact explicit expressions as well as recurrence relations for the single and product moments of record values and then use these results to compute the means,variances...Based on lower record values,we first derive the exact explicit expressions as well as recurrence relations for the single and product moments of record values and then use these results to compute the means,variances and coefficient of skewness and kurtosis of exponentiated moment exponential distribution(EMED),a new extension of moment exponential distribution,recently introduced by Hasnain(Exponentiated moment exponential distribution.Ph.D.Thesis,2013).Next we obtain the maximum likelihood estimators of the unknown parameters and the approximate confidence intervals of the EMED.Finally,we consider Bayes estimation under the symmetric and asymmetric loss functions using gamma priors for both shape and scale parameters.We have also derived the Bayes interval of this distribution and discussed both frequentist and the Bayesian prediction intervals of the future record values based on the observed record values.Monte Carlo simulations are performed to compare the performances of the proposed methods,and a data set has been analyzed for illustrative purposes.展开更多
The quantile-based entropy measures possess some unique properties than their distribution function approach.The present communication deals with the study of the quantile-based Shannon entropy for record statistics.I...The quantile-based entropy measures possess some unique properties than their distribution function approach.The present communication deals with the study of the quantile-based Shannon entropy for record statistics.In this regard a generalized model is considered for which cumulative distribution function or probability density function does not exist and various examples are provided for illustration purpose.Further we consider the dynamic versions of the proposed entropy measure for record statistics and also give a characterization result for that.At the end,we study F^(α)-family of distributions for the proposed entropy measure.展开更多
文摘In this paper, we derive the distributions of concomitants of record values from generalized Farlie-Gumbel-Morgenstern family of bivariate distributions. We derive the single and the product moments of the concomitants for the general case. The results are then applied to the ease of the two-parameter exponential marginal distributions. Using concomitants of record values we derive the best linear unbiased estimators of parameters of the marginal distributions. Moreover, two methods for obtaining predictors of concomitants of record values are presented. Finally, a numerical illustration is performed to highlight the theoretical results obtained.
文摘The power generalized Weibull distribution has been proposed recently by[24]as an alternative to the gamma,Weibull and the exponentiated Weibull distributions.The power generalized Weibull family is suitable for modeling data that indicate nonmonotone hazard rates and can be used in survival analysis and reliability studies.Usefulness andflexibility of the family are illustrated by reanalyzing Efron’s data pertaining to a head-and-neck cancer clinical trial.These data involve censoring and indicate unimodal hazard rate.For this distribution,some recurrence relations are established for the single and product moments of upper record values.Further,using these relations,we have obtained means,variances and covariances of upper record values from samples of sizes up to 10 for various values of the parameters and present them infigures.Real data set is analyzed to illustrate theflexibility and importance of the model.
文摘Based on lower record values,we first derive the exact explicit expressions as well as recurrence relations for the single and product moments of record values and then use these results to compute the means,variances and coefficient of skewness and kurtosis of exponentiated moment exponential distribution(EMED),a new extension of moment exponential distribution,recently introduced by Hasnain(Exponentiated moment exponential distribution.Ph.D.Thesis,2013).Next we obtain the maximum likelihood estimators of the unknown parameters and the approximate confidence intervals of the EMED.Finally,we consider Bayes estimation under the symmetric and asymmetric loss functions using gamma priors for both shape and scale parameters.We have also derived the Bayes interval of this distribution and discussed both frequentist and the Bayesian prediction intervals of the future record values based on the observed record values.Monte Carlo simulations are performed to compare the performances of the proposed methods,and a data set has been analyzed for illustrative purposes.
文摘The quantile-based entropy measures possess some unique properties than their distribution function approach.The present communication deals with the study of the quantile-based Shannon entropy for record statistics.In this regard a generalized model is considered for which cumulative distribution function or probability density function does not exist and various examples are provided for illustration purpose.Further we consider the dynamic versions of the proposed entropy measure for record statistics and also give a characterization result for that.At the end,we study F^(α)-family of distributions for the proposed entropy measure.
