Firstly, the maximum likelihood estimate and asymptotic confidence interval of the unkown parameter for the Topp-Leone distribution are obtained under Type-I left censored samples, furthermore, the asymptotic confiden...Firstly, the maximum likelihood estimate and asymptotic confidence interval of the unkown parameter for the Topp-Leone distribution are obtained under Type-I left censored samples, furthermore, the asymptotic confidence interval of reliability function is obtained based on monotonicity. Secondly, under different loss functions, the Bayesian estimates of the unkown parameter and reliability function are obtained, and the expected mean square errors of Bayesian estimates are calculated. Monte-Carlo method is used to calculate the mean values and relative errors of the estimates. Finally, an example of life data is analyzed by using the statistical method in this paper.展开更多
This paper presents an extended lifetime probability distribution based on the alpha power transformation. We refer to the proposed distribution as “the Alpha Power Topp-Leone (APTL) distribution”. Mathematical prop...This paper presents an extended lifetime probability distribution based on the alpha power transformation. We refer to the proposed distribution as “the Alpha Power Topp-Leone (APTL) distribution”. Mathematical properties of the APTL distribution such as the density and cumulative distribution functions, survival and hazard rate functions, quantile function, median, moments and its relative measures, probability weighted moment, moment generating function, Renyi entropy, and the distribution of order statistics were derived. The method of maximum likelihood estimation was employed to estimate the unknown parameters of the APTL distribution. Finally, we used two real data sets obtained from the literature to illustrate the applicability of the APTL distribution in real-life data fitting.展开更多
In this paper,we introduce a modified family of distributions that unifies three different families with only one tuning parameter;the so-called exp-G,Topp–Leone-G and exp-half-G families of distributions.We study ma...In this paper,we introduce a modified family of distributions that unifies three different families with only one tuning parameter;the so-called exp-G,Topp–Leone-G and exp-half-G families of distributions.We study mathematical properties of the proposed family,including linear representations,quantile function,probability weighted moments,reliability parameter and stochastic ordering.One of the corresponding parametric statistical model is outlined,with estimation of the parameters by the method of maximum likelihood and investigation for possible applications to glycosaminoglycans concentration level in urine over the beta Weibull and Kumaraswamy Weibull distributions.The goodness-of-fit of five other members of the family is also assessed.Regression model is also discussed using the proposed distribution and applied to establish the relationship between the glycosaminoglycans concentration level and age of the children.展开更多
We introduce a new two-parameter model related to the inverted Topp–Leone distribution called the power inverted Topp–Leone(PITL)distribution.Major properties of the PITL distribution are stated;including;quantile m...We introduce a new two-parameter model related to the inverted Topp–Leone distribution called the power inverted Topp–Leone(PITL)distribution.Major properties of the PITL distribution are stated;including;quantile measures,moments,moment generating function,probability weighted moments,Bonferroni and Lorenz curve,stochastic ordering,incomplete moments,residual life function,and entropy measure.Acceptance sampling plans are developed for the PITL distribution,when the life test is truncated at a pre-specified time.The truncation time is assumed to be the median lifetime of the PITL distribution with pre-specified factors.The minimum sample size necessary to ensure the specified life test is obtained under a given consumer’s risk.Numerical results for given consumer’s risk,parameters of the PITL distribution and the truncation time are obtained.The estimation of the model parameters is argued using maximum likelihood,least squares,weighted least squares,maximum product of spacing and Bayesian methods.A simulation study is confirmed to evaluate and compare the behavior of different estimates.Two real data applications are afforded in order to examine the flexibility of the proposed model compared with some others distributions.The results show that the power inverted Topp–Leone distribution is the best according to the model selection criteria than other competitive models.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11901058).
文摘Firstly, the maximum likelihood estimate and asymptotic confidence interval of the unkown parameter for the Topp-Leone distribution are obtained under Type-I left censored samples, furthermore, the asymptotic confidence interval of reliability function is obtained based on monotonicity. Secondly, under different loss functions, the Bayesian estimates of the unkown parameter and reliability function are obtained, and the expected mean square errors of Bayesian estimates are calculated. Monte-Carlo method is used to calculate the mean values and relative errors of the estimates. Finally, an example of life data is analyzed by using the statistical method in this paper.
文摘This paper presents an extended lifetime probability distribution based on the alpha power transformation. We refer to the proposed distribution as “the Alpha Power Topp-Leone (APTL) distribution”. Mathematical properties of the APTL distribution such as the density and cumulative distribution functions, survival and hazard rate functions, quantile function, median, moments and its relative measures, probability weighted moment, moment generating function, Renyi entropy, and the distribution of order statistics were derived. The method of maximum likelihood estimation was employed to estimate the unknown parameters of the APTL distribution. Finally, we used two real data sets obtained from the literature to illustrate the applicability of the APTL distribution in real-life data fitting.
基金the financial support from Science and Engineering Research Board,Department of Science&Technology,Govt,of India,under the scheme Early Career Research Award(file no.:ECR/2017/002416).
文摘In this paper,we introduce a modified family of distributions that unifies three different families with only one tuning parameter;the so-called exp-G,Topp–Leone-G and exp-half-G families of distributions.We study mathematical properties of the proposed family,including linear representations,quantile function,probability weighted moments,reliability parameter and stochastic ordering.One of the corresponding parametric statistical model is outlined,with estimation of the parameters by the method of maximum likelihood and investigation for possible applications to glycosaminoglycans concentration level in urine over the beta Weibull and Kumaraswamy Weibull distributions.The goodness-of-fit of five other members of the family is also assessed.Regression model is also discussed using the proposed distribution and applied to establish the relationship between the glycosaminoglycans concentration level and age of the children.
文摘We introduce a new two-parameter model related to the inverted Topp–Leone distribution called the power inverted Topp–Leone(PITL)distribution.Major properties of the PITL distribution are stated;including;quantile measures,moments,moment generating function,probability weighted moments,Bonferroni and Lorenz curve,stochastic ordering,incomplete moments,residual life function,and entropy measure.Acceptance sampling plans are developed for the PITL distribution,when the life test is truncated at a pre-specified time.The truncation time is assumed to be the median lifetime of the PITL distribution with pre-specified factors.The minimum sample size necessary to ensure the specified life test is obtained under a given consumer’s risk.Numerical results for given consumer’s risk,parameters of the PITL distribution and the truncation time are obtained.The estimation of the model parameters is argued using maximum likelihood,least squares,weighted least squares,maximum product of spacing and Bayesian methods.A simulation study is confirmed to evaluate and compare the behavior of different estimates.Two real data applications are afforded in order to examine the flexibility of the proposed model compared with some others distributions.The results show that the power inverted Topp–Leone distribution is the best according to the model selection criteria than other competitive models.
