Half Logistic Distribution Research Articles

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.

A study of stress-strength reliability using a generalization of power transformed half-logistic distribution

A new probability model obtained by generalizing the power transformed half logistic distribution is introduced by transforming the type II beta distribution. The basic properties of the distribution are studied and observed that the distribution can be used for modeling heavy tailed data. Further the expression for stress strength reliability of a single component system with strength following the proposed model and different cases for stress are obtained. Different methods of estimation of parameters – method of moments, quantile estimation, and maximum likelihood estimation are also explained. The usefulness of the model is also studied by applying it to a real-life data set.

The Beta Type I Generalized Half Logistic Distribution: Properties and Application

In a view to obtain a new distribution that is more exible than the type I generalized half logistic distribution, we used the beta-G generator and the type I generalized half logistic distribution. Some properties of the new distribution including the cummulative distribution function,survival function, hazard function were studied. Estimation of parameters were done using the maximum likelihood estimation method. Application of the derived distribution to lifetime data was illustrated by applying to remission times of bladder cancer patient data and survival times of guinea pigs.

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 Properties and Different Methods of Estimation for Type I Half Logistic Inverted Kumaraswamy Distribution

In this paper, we introduce and study a new three-parameter lifetime distribution constructed from the so-called type I half-logistic-G family and the inverted Kumaraswamy distribution, naturally called the type I half-logistic inverted Kumaraswamy distribution. The main feature of this new distribution is to add a new tuning parameter to the inverted Kumaraswamy (according to the type I half-logistic structure), with the aim to increase the flexibility of the related inverted Kumaraswamy model and thus offering more precise diagnostics in data analyses. The new distribution is discussed in detail, exhibiting various mathematical and statistical properties, with related graphics and numerical results. An exhaustive simulation was conducted to investigate the estimation of the model parameters via several well-established methods, including the method of maximum likelihood estimation, methods of least squares and weighted least squares estimation, and method of Cramer-von Mises minimum distance estimation, showing their numerical efficiency. Finally, by considering the method of maximum likelihood estimation, we apply the new model to fit two practical data sets. In this regards, it is proved to be better than recent models, also derived to the inverted Kumaraswamy distribution.

Bayesian Estimation of Generalized Half-logistic Distribution under Accelerated Life tests with Type-I Censoring,

Bayesian Estimation of Generalized Half-logistic Distribution under Accelerated Life tests with Type-I Censoring,

A New Acceptance Sampling Plans Based on Percentiles For Type II Generalized Half-logistic Distribution

A New Acceptance Sampling Plans Based on Percentiles For Type II Generalized Half-logistic Distribution

Approximate maximum product spacing estimation of half logistic distribution under progressive type II censored samples

Approximate maximum product spacing estimation of half logistic distribution under progressive type II censored samples

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.

A New Two-Parameter Lifetime Distribution: Properties, Applications and Different Method of Estimations

In this paper, we introduce a new two-parameter distribution which is called new Odd Log-Logistic Half-Logistic (NOLL-HL) distribution. Theoretical properties of this model including the hazard function, survival function, asymptotic, extreme value, quantile function, moments, conditional moments, mean residual life, mean past lifetime, coefficients of skewness and kurtosis, 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

Type II half logistic Ibrahim distribution with applications

In this paper, we introduce a new distribution called type II half logistic Ibrahim (TIIHLI) distribution. Some properties of this distribution will be discussed. The estimation of unknown parameters for TIIHLI distribution will be handled using real data. Â

A New Extension of the Generalized Half Logistic Distribution with Applications to Real Data.

In this paper, we introduced a new three-parameter probability model called Poisson generalized half logistic (PoiGHL). The new model possesses an increasing, decreasing, unimodal and bathtub failure rates depending on the parameters. The relationship of PoiGHL with the exponentiated Weibull Poisson (EWP), Poisson exponentiated Erlang-truncated exponential (PEETE), and Poisson generalized Gompertz (PGG) model is discussed. We also characterized the PoiGHL sub model, i.e the half logistic Poisson (HLP), based on certain functions of a random variable by truncated moments. Several mathematical and statistical properties of the PoiGHL are investigated such as moments, mean deviations, Bonferroni and Lorenz curves, order statistics, Shannon and Renyi entropy, Kullback-Leibler divergence, moments of residual life, and probability weighted moments. Estimation of the model parameters was achieved by maximum likelihood technique and assessed by simulation studies. The stress-strength analysis was discussed in detail based on maximum likelihood estimation (MLE), we derived the asymptotic confidence interval of based on the MLEs, and examine by simulation studies. In three applications to real data set PoiGHL provided better fit and outperform some other popular distributions. In the stress-strength parameter estimation PoiGHL model illustrated as a reliable choice in reliability analysis as shown using two real data set.

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.

On the Flexibility of a Transmuted Type I Generalized Half Logistic Distribution with Application

In this article we transmute the type I half logistic distribution using quadratic rank transmutation map to develop a transmuted type I half logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its baseline distribution to enhance more flexibility in the analysis of data in various disciplines such as reliability analysis in engineering, survival analysis, medicine, biological sciences, actuarial science, finance and insurance. The mathematical properties such as moments, quantile, mean, median, variance, skewness and kurtosis of this distribution are discussed. The reliability and hazard functions of the transmuted type I half logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the transmuted type I half logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density function of the transmuted type I half logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using it to fit relevant data. The study is concluded by demonstrating that the transmuted type I half logistic distribution has a better goodness of fit than its parent model. We hope this model will serve as an alternative to the existing ones in the literature in fitting positive real data.

On Type II Half Logistic Weibull Distribution with Applications

In recent years, several of new improved and extended probability distributions have been discovered from the current distributions to facilitate their applications in many fields. A new three-parameter distribution, the so called the T ype II half logistic Weibull (TIIHLW), is introduced for modeling lifetime data. Some mathematical properties of the TIIHLW distribution are provided. Explicit expressions for the moments, probability weighted moments, quantile function, order statistics and Renyi entropy are investigated. Maximum likelihood estimation technique is employed to estimate the model parameters and simulation issues are presented. In addition, the superiority of the subject distribution is illustrated with an application to two real data sets. Indeed, the TIIHLW model yields a better fit to these data than the beta Weibull, Mcdonald Weibull and exponentiated Weibull distributions. Keywords : Type II half logistic-G class; Weibull distribution, Order statistics; Maximum likelihood method. DOI : 10.7176/MTM/9-1-05

A Study on Transmuted Half Logistic Distribution: Properties and Application

In this article we transmute the half logistic distribution using quadratic rank transmutation map to develop a transmuted half logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its baseline distribution to enhance more flexibility in the analysis of data in various disciplines such as reliability analysis in engineering, survival analysis, medicine, biological sciences, actuarial science, finance and insurance. The mathematical properties such as moments, quantile, mean, median, variance, skewness and kurtosis of this distribution are discussed. The reliability and hazard functions of the transmuted half logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the transmuted half logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density function of the transmuted half logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using it to fit relevant data. The study is concluded by demonstrating that the transmuted half logistic distribution has a better goodness of fit than its parent model. We hope this model will serve as an alternative to the existing ones in the literature in fitting positive real data.

Teori ve Uygulamaları ile Marshall-Olkin Yarı Lojistik Dağılımı

In this study we present a new distribution named as Marshall-Olkin Half Logistic (MOHL) by extending half logistic distribution to increase the flexibility. We derive some fundamental properties including survival function, hazard rate function, skewness, kurtosis, order statistics and entropy function. Parameters are estimated using maximum likelihood estimation method to fit new model. Then, a simulation study is conducted to show the performance of the proposed model.

Maximum Likelihood and Bayesian Estimation for Two-Parameter Type I Half Logistic Lindley Distribution

Maximum Likelihood and Bayesian Estimation for Two-Parameter Type I Half Logistic Lindley Distribution

Comparative Study of the Non-Homogeneous Poisson Process Type-I Generalized Half-Logistic Distribution

In this paper, Non-Homogeneous Poisson Process (NHPP) model are created based on Type-I Generalized Half-Logistic Distribution (GHLD- I). Three methods for estimating the parameters of the NHPP GHLD- I model are considered in the case of failure-occurrence time data, for this purpose the necessary likelihood equations are obtained. Confidence intervals are studied, the upper and the lower bounds of the parameters are constructed. An application based on the NHPP GHLD-I and using four published data sets are conducted. The performance of NHPP GHLD-I model is checked based on three evaluation criteria and useful results are obtained.