Exponentiated Half Logistic Distribution Research Articles

Bivariate exponentiated half logistic distribution: Properties and application

The exponentiated half logistic (EHL) distribution can be mostly and effectively used in modeling lifetime data. It is very similar to the gamma and exponentiated exponential distributions with two parameters. The major advantage of EHL distribution over the gamma distribution is that its cumulative distribution has a closed form. In this research, we develop a new bivariate exponentiated half logistic (BEHL) distribution with univariate EHL distribution as the marginals. The joint probability density function and the joint cumulative distribution function were expressed in explicit forms. This article also presents the various properties of the proposed distribution such as marginal, conditional distributions and product moments. The maximum likelihood estimates for the unknown parameters of BEHL distribution and their approximate variance- covariance matrix have been obtained. Monte Carlo simulations have been conducted to check the performances of the maximum likelihood estimators with applications to a real data set. Analysis showed that the BEHL distribution gives a better fit than other rival bivariate probability models.

Estimation of the exponentiated half-logistic distribution based on multiply Type-I hybrid censoring

In this paper, we derive some estimators of the scale parameter of the exponentiated half-logistic distribution based on the multiply Type-I hybrid censoring scheme. We assume that the shape parameter λ is known. We obtain the maximum likelihood estimator of the scale parameter σ. The scale parameter is estimated by approximating the given likelihood function using two different Taylor series expansions since the likelihood equation is not explicitly solved. We also obtain Bayes estimators using prior distribution. To obtain the Bayes estimators, we use the squared error loss function and general entropy loss function (shape parameter q = -0.5, 1.0). We also derive interval estimation such as the asymptotic confidence interval, the credible interval, and the highest posterior density interval. Finally, we compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. The average length of 95% intervals and the corresponding coverage probability are also obtained.

Design of multiple-deferred state sampling plans for exponentiated half logistic distribution

This paper aims to develop a multiple deferred state sampling plan for a time-truncated life test if the lifetime of the item follows exponentiated half logistic distribution. The optimal parameters of the proposed plan, such as the number of successive lots required for making the decision whether to accept or reject the current lot, sample size, the rejection and acceptance numbers are obtained using two points approach. The implementation of the proposed plan is illustrated with examples. Tables are constructed for various combinations of consumer’s and producer’s risks. Comparison is also made with existing sampling plans under exponentiated half logistic distribution.

Statistical inference for the exponentiated half logistic distribution based on censored data

In this paper, we consider the estimates for the scale parameter of an exponentiated half logistic distribution under progressively Type-II censoring and general progressively Type-II censoring, respectively. Because of the complex form of the traditional maximum likelihood estimator, it is hard to get an explicit solution. Therefore, we propose three new estimation methods based on censored data to obtain approximate estimates of the scale parameter. The first two are approximate maximum likelihood estimation methods based on Taylor expansion and the third is the approximate estimation method based on pivotal quantities we establish. Furthermore, we consider asymptotic confidence intervals based on pivotal quantities. Finally, simulation studies are conducted to compare the performance of the proposed estimators. A real dataset analysis is carried out to illustrate the proposed methods.

Inference for an exponentiated half logistic distribution with application to cancer hybrid censored data

In this paper, based on hybrid censored sample from a two parameter exponentiated half logistic distribution, we consider the problem of estimating the unknown parameters using frequentist and Bayesian approaches. Expectation-Maximization, Lindley’s approximation and Metropolis-Hastings algorithms are used for obtaining point estimators and corresponding confidence intervals for the shape and scale parameters involved in the underlying model. Data analyses involving the survival times of patients suffering from cancer diseases and treated radiotherapy and/or chemotherapy have been performed. Finally, numerical simulation study was conducted to assess the performances of the so developed methods and conclusions on our findings are reported.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

A Control Chart for Time Truncated Life Tests Using Exponentiated Half Logistic Distribution

A Control Chart for Time Truncated Life Tests Using Exponentiated Half Logistic Distribution

Exponentiated half logistic distribution: Different estimation methods and joint confidence regions

ABSTRACTIn this article, we study the problem of estimating the unknown shape and scale parameters of the exponentiated half logistic distribution. For the maximum-likelihood estimation, we obtain a necessary and sufficient condition for the existence and uniqueness of maximum-likelihood estimates of the parameters. Inverse moment and modified inverse moment estimators are derived. Monte Carlo simulations are conducted to compare their performances. Two methods for constructing joint confidence regions for the two parameters are also proposed and their performances are discussed. A numerical example is presented to illustrate the methods.

More efficient approaches to the exponentiated half-logistic distribution based on record values.

The exponentiated half-logistic distribution has various shapes depending on its shape parameter. Therefore, this paper proposes more efficient approach methods for estimating shape parameters in the presence of a nuisance parameter, that is, a scale parameter, from Bayesian and non-Bayesian perspectives if record values have an exponentiated half-logistic distribution. In the frequentist approach, estimation methods based on pivotal quantities are proposed which require no complex computation unlike the maximum likelihood method. In the Bayesian approach, a robust estimation method is developed by constructing a hierarchical structure of the parameter of interest. In addition, two approaches address how the nuisance parameter can be dealt with and verifies that the proposed methods are more efficient than existing methods through Monte Carlo simulations and analyses based on real data.

Bayesian and maximum likelihood estimations of the inverted exponentiated half logistic distribution under progressive Type II censoring

ABSTRACTIn this paper, the estimation of parameters, reliability and hazard functions of a inverted exponentiated half logistic distribution (IEHLD) from progressive Type II censored data has been considered. The Bayes estimates for progressive Type II censored IEHLD under asymmetric and symmetric loss functions such as squared error, general entropy and linex loss function are provided. The Bayes estimates for progressive Type II censored IEHLD parameters, reliability and hazard functions are also obtained under the balanced loss functions. However, the Bayes estimates cannot be obtained explicitly, Lindley approximation method and importance sampling procedure are considered to obtain the Bayes estimates. Furthermore, the asymptotic normality of the maximum likelihood estimates is used to obtain the approximate confidence intervals. The highest posterior density credible intervals of the parameters based on importance sampling procedure are computed. Simulations are performed to see the performance of the proposed estimates. For illustrative purposes, two data sets have been analyzed.

Group acceptance sampling plans for resubmitted lots under exponentiated half logistic distribution

In this article, we developed a resubmitted lot for group acceptance sampling plan to ensure the lifetime of the product quality assuming that the product lifetime follows the exponentiated half logistic distribution. The plan parameters are determined by fixing the experiment termination time and the number of testers at the specified producer’s and consumer’s risks both satisfy simultaneously. The proposed group sampling plan is compared with the ordinary group sampling plan. An example is given to illustrate the methodology.

An Exponentiated Half Logistic Distribution to Develop a Group Acceptance Sampling Plans with Truncated Time

In this article, we considered a group acceptance sampling plans for exponentiated half logistic distribution if the lifetime is truncated at a pre-assigned time with known index parameter of the exponentiated half logistic distribution. The number of groups and the acceptance number of suggested sampling plan are determined when both the producer's and consumer's risks are conforming to at the fixed quality points, the termination time and the number of components in each group with regard to percentiles. Finally, an example is given to illustration the methodology.

Notes on the exponentiated half logistic distribution

In this paper moment estimators and maximum likelihood estimators of unknown parameters in the exponentiated half-logistic distribution are derived, and an entropy estimator is obtained for the distribution. An exact expression of Fisher information is derived to obtain approximate confidence intervals for unknown parameters in the distribution, and for illustration purposes, the validity of the proposed estimation method is assessed using real data.

Bayesian analysis of an exponentiated half-logistic distribution under progressively type-II censoring

Abstract This paper develops maximum likelihood estimators (MLEs) of unknown param-eters in an exponentiated half-logistic distribution based on a progressively type-IIcensored sample. We obtain approximate con dence intervals for the MLEs by usingasymptotic variance and covariance matrices. Using importance sampling, we obtainBayes estimators and corresponding credible intervals with the highest posterior densityand Bayes predictive intervals for unknown parameters based on progressively type-IIcensored data from an exponentiated half logistic distribution. For illustration pur-poses, we examine the validity of the proposed estimation method by using real andsimulated data.Keywords: Bayes predictive interval, exponentiated half-logistic distribution, HPD cred-ible interval, importance sampling, progressively type-II censored sample. 1. Introduction Many reliability and survival analysis studies have used half-logistic distributions, partic-ularly for censored data. Several studies have drawn inferences about half logistic distribu-tions. Balakrishnan and Puthenpura (1986) introduce the best linear unbiased estimator oflocation and scale parameters of half-logistic distributions by considering linear functionsof order statistics. Balakrishnan and Wong (1991) obtain approximate maximum likelihoodestimators (AMLEs) of location and scale parameters of half-logistic distributions by usinga type-II right-censored sample. Kang et al. (2008) derive AMLEs and MLEs of scale pa-rameters of half-logistic distributions by using progressively type-II censored samples. Kanget al. (2009) propose AMLEs of scale parameters of half-logistic distributions by consideringdouble-hybrid censored samples. Kang and Seo (2011) recently examine exponentiated half-logistic distributions and propose two types of AMLEs of scale parameters and reliabilityfunctions by using progressively type-II right-censored samples. Kim et al. (2011a) deriveBayesian estimators of shape parameters, reliability functions, and failure rate functions

Parameter and reliability estimation for an exponentiated half-logistic distribution under progressive type II censoring

In this article, we deal with a two-parameter exponentiated half-logistic distribution. We consider the estimation of unknown parameters, the associated reliability function and the hazard rate function under progressive Type II censoring. Maximum likelihood estimates (M LEs) are proposed for unknown quantities. Bayes estimates are derived with respect to squared error, linex and entropy loss functions. Approximate explicit expressions for all Bayes estimates are obtained using the Lindley method. We also use importance sampling scheme to compute the Bayes estimates. Markov Chain Monte Carlo samples are further used to produce credible intervals for the unknown parameters. Asymptotic confidence intervals are constructed using the normality property of the MLEs. For comparison purposes, bootstrap-p and bootstrap-t confidence intervals are also constructed. A comprehensive numerical study is performed to compare the proposed estimates. Finally, a real-life data set is analysed to illustrate the proposed methods of estimation.

Estimation in an Exponentiated Half Logistic Distribution under Progressively Type-II Censoring

In this paper, we derive the maximum likelihood estimator(MLE) and some approximate maximum likelihood estimators(AMLEs) of the scale parameter in an exponentiated half logistic distribution based on progressively Type-II censored samples. We compare the proposed estimators in the sense of the mean squared error(MSE) through a Monte Carlo simulation for various censoring schemes. We also obtain the AMLEs of the reliability function.