Half Logistic Distribution Research Articles

Product spacing estimation of half logistic distribution under progressive hybrid censoring

In most of the life testing and reliability experiments, the experimenter is often, unable to observe life time of all items put on test and the data avilable to the experimenter is censored data. Among these censoring schemes, progressive censoring (PrC) is gaining rapid popularity. However, the drawback of the PrC is that it might take a very long time in order to complete the life test. In this reason, the progressive hybrid censoring scheme (PrHcs) was proposed. In this paper, we derive the maximum product spacings estimators (MaxPE) for the unknown parameter and reliability function (ReFtn) of half logistic distribution (HalfLD) under the PrHcs. And we derive the approximate maximum product spacings estimators (AppMaxPE) for the unknown parameter and ReFtn of HalfLD using Talyor series expansion. We also compare the estimators of unknown parameter and ReFtn in the terms of the mean squared error (MeanSqE) and bias for various PrHcs. In addition, real data example based on the PrHcs have been also analysed for illustrative purposes.

A New Type I Half-Logistic Inverse Weibull Distribution with an Application to the Relief Times Data of Patients Receiving an Analgesic

This article presents a new extension of the type I half-logistic inverse Weibull distribution. It is used as a base line to construct a new bivariate model that is called bivariate extended type I half-logistic inverse Weibull model. Statistical properties of the proposed distributions are derived in explicit forms. Maximum likelihood estimators are discussed. Simulation is employed to discuss theoretical properties, to investigate the performance of the new models and to elaborate the goodness of fit. The new models are applied to real data sets.

Multiple dependent state repetitive sampling plans for exponentiated half logistic distribution

ABSTRACT In the textile and packing industries, the lifetime of the items is exhibited by some statistical distribution. This paper aims to develop a multiple dependent state repetitive (MDSR) sampling plan by assuming that the lifetime of an item comes from an exponentiated half logistic distribution (EHLD). The MDSR sampling plan will be more economical than the other sampling plans on hand such as the multiple dependent state sampling schemes, the repetitive sampling plan, the single sampling plan, and the resubmitted sampling plan concerning the size of the sample required to test the lot. The design parameters for the developed sampling plans are obtained by minimizing the average sample number when both the consumer’s and producer’s risks are satisfied at corresponding quality levels. Tables are given for practical use. The proposed MDSR sampling plan is compared with the single sampling plan and some examples are also provided.

New compounding lifetime distributions with applications to real data

Motivation to fit the Danish reinsurance claim and aircraft windshield data sets, we introduce exponentiated half logistic-power series (EHLPS) distributions, which are obtained by compounding exponentiated half-logistic distribution with power series distributions. Some mathematical properties have been studied. Maximum likelihood estimation of unknown parameters for the complete data is discussed via the EM algorithm. Simulation results to assess the performance of the estimation methods are discussed. Finally, two applied examples are given for indicating the flexibility and appropriateness of the distribution.

Estimations of accelerated generalized half-logistic distribution in presence of generalized type-II hybrid censoring samples

Generally, the analysis of a lifetime data to quantify the life characteristics of the product done under normal conditions. The engineers for some reasons may be needed to obtain the reliability results more quickly then, accelerated life tests are applied. In this paper, we adopted partially step-stress accelerated life tests model of product has the generalized half-logistic lifetime distribution. This model is ap?plied on a solar lighting device and the stress factor consider to be temperature. Also, to save the minimum and maximum ideal test time, we applied the general?ized type-II hybrid censoring scheme. The parameters of the proposed model are estimated by maximum likelihood and Bayes methods for point and corresponding interval estimators. The validity of results is tested under formulation Monte-Carlo simulation study. The proposed model is applied on analysis data obtained from solar lighting device as real data set for illustrative purposes.

Classical and Bayesian Inference of an Exponentiated Half-Logistic Distribution under Adaptive Type II Progressive Censoring.

The point and interval estimations for the unknown parameters of an exponentiated half-logistic distribution based on adaptive type II progressive censoring are obtained in this article. At the beginning, the maximum likelihood estimators are derived. Afterward, the observed and expected Fisher’s information matrix are obtained to construct the asymptotic confidence intervals. Meanwhile, the percentile bootstrap method and the bootstrap-t method are put forward for the establishment of confidence intervals. With respect to Bayesian estimation, the Lindley method is used under three different loss functions. The importance sampling method is also applied to calculate Bayesian estimates and construct corresponding highest posterior density (HPD) credible intervals. Finally, numerous simulation studies are conducted on the basis of Markov Chain Monte Carlo (MCMC) samples to contrast the performance of the estimations, and an authentic data set is analyzed for exemplifying intention.

A New Extended Cosine—G Distributions for Lifetime Studies

In this article, we introduce a new extended cosine family of distributions. Some important mathematical and statistical properties are studied, including asymptotic results, a quantile function, series representation of the cumulative distribution and probability density functions, moments, moments of residual life, reliability parameter, and order statistics. Three special members of the family are proposed and discussed, namely, the extended cosine Weibull, extended cosine power, and extended cosine generalized half-logistic distributions. Maximum likelihood, least-square, percentile, and Bayes methods are considered for parameter estimation. Simulation studies are used to assess these methods and show their satisfactory performance. The stress–strength reliability underlying the extended cosine Weibull distribution is discussed. In particular, the stress–strength reliability parameter is estimated via a Bayes method using gamma prior under the square error loss, absolute error loss, maximum a posteriori, general entropy loss, and linear exponential loss functions. In the end, three real applications of the findings are provided for illustration; one of them concerns stress–strength data analyzed by the extended cosine Weibull distribution.

Sine Half-Logistic Inverse Rayleigh Distribution: Properties, Estimation, and Applications in Biomedical Data

A new lifetime distribution with two parameters, known as the sine half-logistic inverse Rayleigh distribution, is proposed and studied as an extension of the half-logistic inverse Rayleigh model. The sine half-logistic inverse Rayleigh model is a new inverse Rayleigh distribution extension. In the application section, we show that the sine half-logistic inverse Rayleigh distribution is more flexible than the half-logistic inverse Rayleigh and inverse Rayleigh distributions. The statistical properties of the half-logistic inverse Rayleigh model are calculated, including the quantile function, moments, moment generating function, incomplete moment, and Lorenz and Bonferroni curves. Entropy measures such as Rényi entropy, Havrda and Charvat entropy, Arimoto entropy, and Tsallis entropy are proposed for the sine half-logistic inverse Rayleigh distribution. To estimate the sine half-logistic inverse Rayleigh distribution parameters, statistical inference using the maximum likelihood method is used. Applications of the sine half-logistic inverse Rayleigh model to real datasets demonstrate the flexibility of the sine half-logistic inverse Rayleigh distribution by comparing it to well-known models such as half-logistic inverse Rayleigh, type II Topp–Leone inverse Rayleigh, transmuted inverse Rayleigh, and inverse Rayleigh distributions.

Estimation of the exponentiated half-logistic distribution under generalized type I hybrid censored samples

In this paper, we consider the shape parameter for the exponentiated half logistic distribution (ExHL) when samples are generalized type I hybrid censored samples. The shape parameter for the ExHL is estimated by the Bayesian method. We consider conjugate prior and corresponding posterior distribution is obtained. We also obtain the maximum likelihood estimator (MLE) of the shape parameter under the generalized type I hybrid censored samples (GenT1HCs). We compare the estimators in the sense of the root mean square error (RMSE). The simulation procedure is repeated 1,000 times for the sample size n = 20, 30, 40 and various generalized type I hybrid censored samples. Finally, a real data set has been analysed for illustrative purpose.

The Type I Half Logistic Skew-t Distribution: A Heavy-Tail Model with Inverted Bathtub Shaped Hazard Rate

In this article a new generalization of the skew student-t distribution was introduced. The two-parameter model called the type I half-logistic skew-t (TIHLST) distribution can fit skewed, heavy-right tail, and long-tail datasets. Statistical properties of the type I half-logistic skew-t (TIHLST) distribution were derived and the maximum likelihood method parameter estimates assessed through a simulation study. A well-known dataset was analysed, illustrating the usefulness of the new distribution in modeling skewed and heavy-tailed data. The hazard rate shape was found to be increasing, decreasing and inverted bathtub shaped which was also reflected in the application result.

Designing of multiple dependent state repetitive sampling plan for type-II generalized half logistic distribution

Designing of multiple dependent state repetitive sampling plan for type-II generalized half logistic distribution

A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations

Abstract In this paper, we introduce a new two-parameter lifetime distribution which is called extended Half-Logistic (EHL) distribution. Theoretical properties of this model including the hazard function, quantile function, asymptotic, extreme value, moments, conditional moments, mean residual life, mean past lifetime, residual entropy, cumulative residual entropy and order statistics are derived and studied in details. The maximum likelihood estimates of parameters are compared with various methods of estimations by conducting a simulation study. Finally, two real data sets are illustration the purposes.

Time-Dependent Stress-Strength Reliability Model with Phase-Type Cycle Time Based on Finite Mixture Models

This paper deals with the estimation of the stress-strength reliability of time-dependent models. Suppose that a system is allowed to run continuously and is subjected to random stress at random time points. Then we can assume a decrease in the strength of the system during the completion of each run. Let the strength of the system decreases by a constant and the stress on the system increases by a constant over each run. Time taken for completion of a run is assumed to have continuous phase-type distribution, the initial strength of the system, as well as, initial stress on the system are assumed to have a finite mixture of either Weibull distributions or power transformed half logistic distributions. A detailed numerical illustration of the results is also carried out.

A New Two-parameter Modified Half-logistic Distribution: Properties and Applications

This article aims to present and analyse a modified two-parameter version of the Half-Logistic lifetime model.The hazard function, quantile function, asymptotic, linear combination, extreme value, moments, incomplete moments, residual entropies, moment generating function and order statistics, all theoretical properties of this model that are derived and discussed in depth. By performing a simulation analysis, the various techniques of estimation are compared to the estimates of the maximum likelihood of parameters.Finally, two actual data sets have been applied to illustrate the goals of this article.

일반화된 조정 점진적 복합 중도절단에서 하프 로지스틱 분포의 추정

생존실험에서 조정 점진적 복합 중도절단 방법은 실험이 종료하기까지 시간이 오래 소요될 수 있다는 단점이 존재한다. 따라서 최근 일반화된 조정 점진적 복합 중도절단 방법이 소개되어졌다. 본 논문은 일반화된 조정 점진적 복합 중도절단에서 하프 로지스틱분포의 모수를 추정하고자 한다. 모수를 추정하는 방법으로 최대우도추정량과 테일러 급수 전개를 이용한 근사 최대우도추정량을 사용하였다. 또한, 대칭손실함수를 이용하여 하프 로지스틱분포의 모수를 추정하였다. 하지만 베이지안 추정량를 정확하게 계산할 수 없어 Tierney와 Kadane의 근사적인 방법을 사용하여 베이지안 추정량을 계산하였다. 그리고 다양한 일반화된 조정 점진정 복합 중도절단 상황에서 모의실험을 통하여 제안한 추정량들의 평균제곱오차와 편의를 계산하여 비교하였다. 마지막으로 사례 자료를 이용하여 제안한 추정량들을 계산하였다.

Group Acceptance Sampling Plans for Resubmitted lots for life tests based on Half Logistic Distribution

In this article, a group acceptance sampling plan (GASP) for lot resubmitting is developed to ensure quality of the product lifetime assuming that the product’s lifetime follows the half logistic distribution. The parameters of the GASP are determined by satifying the specified producer’s and consumer’s risks according to the experiment termination time and the number of testers. A comparison between this proposed group sampling and the ordinary group sampling plan is discussed. This proposed plan is justified with an illustration.

A new one-parameter lifetime distribution and its regression model with applications.

Lifetime distributions are an important statistical tools to model the different characteristics of lifetime data sets. The statistical literature contains very sophisticated distributions to analyze these kind of data sets. However, these distributions have many parameters which cause a problem in estimation step. To open a new opportunity in modeling these kind of data sets, we propose a new extension of half-logistic distribution by using the odd Lindley-G family of distributions. The proposed distribution has only one parameter and simple mathematical forms. The statistical properties of the proposed distributions, including complete and incomplete moments, quantile function and Rényi entropy, are studied in detail. The unknown model parameter is estimated by using the different estimation methods, namely, maximum likelihood, least square, weighted least square and Cramer-von Mises. The extensive simulation study is given to compare the finite sample performance of parameter estimation methods based on the complete and progressive Type-II censored samples. Additionally, a new log-location-scale regression model is introduced based on a new distribution. The residual analysis of a new regression model is given comprehensively. To convince the readers in favour of the proposed distribution, three real data sets are analyzed and compared with competitive models. Empirical findings show that the proposed one-parameter lifetime distribution produces better results than the other extensions of half-logistic distribution.

Inference and Optimal Design of Accelerated Life Test using Geometric Process for Generalized Half-Logistic Distribution under Progressive Type-II Censoring

Inference and Optimal Design of Accelerated Life Test using Geometric Process for Generalized Half-Logistic Distribution under Progressive Type-II Censoring

Half Logistic Inverse Lomax Distribution with Applications

The last years have revealed the importance of the inverse Lomax distribution in the understanding of lifetime heavy-tailed phenomena. However, the inverse Lomax modeling capabilities have certain limits that researchers aim to overcome. These limits include a certain stiffness in the modulation of the peak and tail properties of the related probability density function. In this paper, a solution is given by using the functionalities of the half logistic family. We introduce a new three-parameter extended inverse Lomax distribution called the half logistic inverse Lomax distribution. We highlight its superiority over the inverse Lomax distribution through various theoretical and practical approaches. The derived properties include the stochastic orders, quantiles, moments, incomplete moments, entropy (Rényi and q) and order statistics. Then, an emphasis is put on the corresponding parametric model. The parameters estimation is performed by six well-established methods. Numerical results are presented to compare the performance of the obtained estimates. Also, a simulation study on the estimation of the Rényi entropy is proposed. Finally, we consider three practical data sets, one containing environmental data, another dealing with engineering data and the last containing insurance data, to show how the practitioner can take advantage of the new half logistic inverse Lomax model.

Inference on the Beta Type I Generalized Half Logistic Distribution Under Right Censored Observation with Application to Covid-19

Inference on the Beta Type I Generalized Half Logistic Distribution Under Right Censored Observation with Application to Covid-19