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Abstract.This article presents several point estimation and interval estimation methods for the Topp-Leone distribution and applies them to the stress-strength model. A new moment estimation and inverse estimation are derived. The algorithm of the maximum likelihood estimation is discussed. Using the generalized pivotal quantity method, the generalized confidence intervals for model parameters and some reliability metrics are also obtained. For the estimation on reliability of stress-strength model, the generalized confidence intervals and bootstrap-p confidence intervals are given. The performance of the proposed methods is assessed by Monte Carlo simulation. Finally, a real example is used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

The study aims to estimate stress strength reliability, denoted as P = P(X > Y ), where X and Y represent a system’s strength and stress parameters, using progressively type-II censoring. Maximum likelihood estimation is used to obtain estimates of stress strength reliability and asymptotic confidence intervals for different parameters and censoring schemes. Bootstrapped confidence intervals (boot-p and boot-t) are also calculated for the same purpose. The Bayesian approach is explored, utilizing Lindley’s and Gibbs’s sampling methods to obtain Bayes’s reliability estimates. Additionally, Bayesian credible intervals and highest posterior density credible intervals are constructed. The accuracy of the various estimates is evaluated through a comprehensive simulation study. Finally, a real data study is presented to validate the proposed methodology further. [ABSTRACT FROM AUTHOR]

In this paper, the Bayesian and non-Bayesian estimation of $$\psi = P(X \gt Y)$$ ψ = P (X > Y) based on the progressively first-failure censored data is considered. The $$X$$ X and $$Y$$ Y are strength and stress random variables and follow the Topp-Leone distributions, respectively. The maximum likelihood and Bayes estimators of $$\psi $$ ψ are derived. The Bayes estimators under generalized entropy loss function are computed using Lindley's approximation and Gibbs sampling methods. Different interval estimates like asymptotic, bootstrap confidence, Bayesian credible, and highest posterior density credible intervals of $$\psi $$ ψ are constructed. Furthermore, a Monte Carlo numerical study is conducted to check the performance of various estimators developed. Finally, an application of algorithm real data is considered for illustrative purposes. [ABSTRACT FROM AUTHOR]

This paper discusses the Topp-Leone-G power series class of distributions. The greatest attention is paid to the investigation of intrinsic characteristic "saturation" to the horizontal asymptote in the Hausdorff sense. Some estimates for the value of the Hausdorff distance are obtained. We present a new family of recurrence generated adaptive functions with corresponding applications. The usefulness of the obtained results is demonstrated in a simulation study of some real data sets from the medical sector and insurance. Some suitable software modules within the programming environment CAS MATHEMATICA are proposed. [ABSTRACT FROM AUTHOR]

The new Ristić and Balakhrisnan or Gamma-Topp-Leone-Type II-Exponentiated Half Logistic-G (RB-TL-TII-EHL-G) family of distributions is introduced and investigated in this paper. This work derives and studies some of the main statistical characteristics of this new family of distributions. The maximum likelihood estimation technique is used to estimate the model parameters, and a simulation study is used to assess the consistency of the estimators. Applications to three real-life datasets from various fields show the value and adaptability of the new RB-TL-TII-EHL-G family of distributions. From our results, it is evident that the new proposed distribution is flexible enough to characterize datasets from different fields compared to several other existing distributions in the literature.

In this work, we proposed a new probability distribution based on the extension of the Gompertz distribution for modeling life time datasets known as the "Topp-Leone Inverse Gompertz Distribution (TLIG distribution)". The TLIG distribution is derived using the logit of Topp-Leone generator and the Inverse Gompertz distribution (IGD) as the baseline distribution. Properties of TLIG distribution were examined. Five different estimation techniques namely maximum likelihood estimate (MLE), Weighted Least Squares Estimates (WLS), Ordinary Least Squares Estimates (OLS), Crammer-Von Miss Estimate (CVME) and Percentile Estimate (PCE) were considered to estimate the parameters of TLIG distribution. A Monte Carlo simulation technique was adopted to assess the consistency and efficiency of these parameter estimates. The usefulness of this new distribution is demonstrated with two real-life datasets whose results shows that the new TLIG distribution performs better than some familiar existing distribution. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we introduce the newly generated Ristić–Balakrishnan–Topp–Leone–Gompertz-G family of distributions. Statistical and mathematical properties of this new family including moments, moment generating function, incomplete moments, conditional moments, probability weighted moments, distribution of the order statistics, stochastic ordering, and Rényi entropy are derived. The unknown parameters of the family are inferred using the maximum likelihood estimation technique. A Monte Carlo simulation study is performed to investigate the convergence of the maximum likelihood estimation. Three real-life data sets are used to demonstrate the flexibility and capacity of the new family of distributions.

This paper introduces and investigates a new family of distributions called the Topp-Leone-Gompertz-exponentiated half logistic-G (TL-Gom-EHL-G) distribution. Some mathematical and statistical properties of this family of distributions are derived. To estimate and evaluate the model parameters, the maximum likelihood estimation technique is used, and the consistency of maximum likelihood estimators is examined using Monte Carlo simulation. Applications to three real data sets from different areas were used to demonstrates the usefulness and versatility of the TL-Gom-EHL-G family of distributions. [ABSTRACT FROM AUTHOR]

In this paper, the inference of multicomponent stress-strength reliability has been derived using progressively censored samples from Topp-Leone distribution. Both stress and strength variables are assumed to follow Topp-Leone distributions with different shape parameters. The maximum likelihood estimate along with the asymptotic confidence interval are developed. Boot-p and Boot-t confidence intervals are also constructed. The Bayes estimates under generalized entropy loss function based on gamma priors using Lindley's, Tierney-Kadane's approximation and Markov chain Monte Carlo methods are derived. A simulation study is considered to check the performance of various estimation methods and different censoring schemes. A real data study shows the applicability of the proposed estimation methods. [ABSTRACT FROM AUTHOR]

The new Ristić and Balakhrisnan or Gamma-Topp-Leone-Type II-Exponentiated Half Logistic-G (RB-TL-TII-EHL-G) family of distributions is introduced and investigated in this paper. This work derives and studies some of the main statistical characteristics of this new family of distributions. The maximum likelihood estimation technique is used to estimate the model parameters, and a simulation study is used to assess the consistency of the estimators. Applications to three real-life datasets from various fields show the value and adaptability of the new RB-TL-TII-EHL-G family of distributions. From our results, it is evident that the new proposed distribution is flexible enough to characterize datasets from different fields compared to several other existing distributions in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the newly generated Ristić–Balakrishnan–Topp–Leone–Gompertz-G family of distributions. Statistical and mathematical properties of this new family including moments, moment generating function, incomplete moments, conditional moments, probability weighted moments, distribution of the order statistics, stochastic ordering, and Rényi entropy are derived. The unknown parameters of the family are inferred using the maximum likelihood estimation technique. A Monte Carlo simulation study is performed to investigate the convergence of the maximum likelihood estimation. Three real-life data sets are used to demonstrate the flexibility and capacity of the new family of distributions. [ABSTRACT FROM AUTHOR]

In this article, a four parameter lifetime model called the Topp–Leone modified Weibull distribution is proposed. The suggested distribution can be considered as an alternative to Kumaraswamy Weibull, generalized modified Weibull, extend odd Weibull Lomax, Weibull-Lomax, Marshall-Olkin alpha power extended Weibull and exponentiated generalized alpha power exponential distributions, etc. The suggested model includes the Topp-Leone Weibull, Topp-Leone Linear failure rate, Topp-Leone exponential and Topp-Leone Rayleigh distributions as a special case. Several characteristics of the new suggested model including quantile function, moments, moment generating function, central moments, mean, variance, coefficient of skewness, coefficient of kurtosis, incomplete moments, the mean residual life and the mean inactive time are derived. The probability density function of the Topp–Leone modified Weibull distribution can be right skewed and uni-modal shaped but, the hazard rate function may be decreasing, increasing, J-shaped, U-shaped and bathtub on its parameters. Three different methods of estimation as; maximum likelihood, maximum product spacing and Bayesian methods are used to estimate the model parameters. For illustrative reasons, applications of the Topp–Leone modified Weibull model to four real data sets related to medical and engineering sciences are provided and contrasted with the fit reached by several other well-known distributions. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and study a new generated family of distributions based on the type II transformation which is called the type II exponentiated half-logistic-Gompertz-Topp-Leone-G (TIIEHL-Gom-TL-G) family of distributions. We investigate its general mathematical properties, including, hazard rate function, quantile function, moments, moment generating function, Rényi entropy and order statistics. Parameter estimates of the new family of distributions are obtained based on the maximum likelihood estimation method and their performance is evaluated via a simulation study. For illustration of the applicability of the new family of distributions, four real data sets are analyzed. [ABSTRACT FROM AUTHOR]

Assuming that the life of the tested samples follows the Topp–Leone distribution, the maximum likelihood estimates and Bayesian estimates of the unknown parameter, reliability and hazard rate are obtained based on the double Type-I hybrid censored samples. According to the observed data, the conditional probability density functions of the future failure moments are obtained, and then the point predictions and interval predictions of the future failure moments are carried out. Based on the double Type-I hybrid censored data, the predictive value and predictive interval of its failure time are given for any tested sample independent and identically distributed in the Topp–Leone distribution. Finally, a numerical example is analysed and the relevant results are calculated. [ABSTRACT FROM AUTHOR]

In this paper, a new class of generalized Lindley distribution called the Topp-Leone Power Lindley distribution (TLPLD) is introduced. Some mathematical properties which include the shape of the density function, hazard rate function, quantile function, moments and related measures, mean deviation, Bonferroni and Lorenz curves, Renyi entropy, distribution of the ordered statistics and Reliability are derived. A lifetime data set is used to illustrate the applicability of the distribution. [ABSTRACT FROM AUTHOR]

In this article, a new generalized distribution named exponentiated inverted Topp-Leone distribution is introduced and some of its properties are presented. Some models of stress strength, quantile, moments, R𝑒́nyi entropy and order statistics are discussed. The relation between exponentiated inverted Topp-Leone distribution and other distributions are derived. The maximum likelihood and Bayes estimators for the parameters, the reliability and hazard rate functions of the exponentiated inverted Topp-Leone distribution based on Type II censored samples are obtained. A simulation study is performed to investigate the effectiveness of the proposed distribution. Finally, a real data set is analyzed to illustrate its flexibility for real-life application. [ABSTRACT FROM AUTHOR]

The Topp-Leone family of univariate distributions has drawn considerable attention in recent years. In this article, we define a bivariate generalization of the Topp-Leone distribution. Moreover, we derive several results such as marginal and conditional distributions, joint moments, correlation coefficient, and Fisher information matrix. Furthermore, we derive the exact distributions of X + Y, X/(X + Y) and XY when X and Y follow bivariate Topp-Leone distribution. [ABSTRACT FROM AUTHOR]

We display the power Topp-Leone (PTL) distribution with two parameters. The following major features of the PTL distribution are investigated: quantile measurements, certain moment's measures, residual life function, and entropy measure. Maximum likelihood, least squares, Cramer von Mises, and weighted least squares approaches are used to estimate the PTL parameters. A numerical illustration is prepared to compare the behavior of the achieved estimates. Data analysis is provided to scrutinize the flexibility of the PTL model matched with Topp-Leone distribution. [ABSTRACT FROM AUTHOR]

In this study, based on progressive type-II censored data, Bayes estimators of the unknown parameter of the Topp-Leone distribution are derived by using informative and noninformative, priors under square error (symmetric), and linex, general entropy, and precautionary (asymmetric) loss functions. The Bayes estimators cannot be obtained in closedforms, for this reason, Lindley's approximation method is used to compute the approximate estimates. The asymptotic confidence and the highest posterior density credible intervals for the unknown parameter are obtained. The performances of the proposed Bayes estimators are compared with the corresponding maximum likelihood estimator for different sample sizes in terms of average estimate and mean squared error through an extensive simulation study. Finally, a real data set is provided to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a five parameter lifetime model called the type II generalized Topp-Leone Dagum distribution. The proposed distribution is a generalization of three parameter Dagum distribution (Type I) using the genesis of type II generalized Topp-Leone family of distributions studied by Hassan et al. (2019). We have obtained some reliability measures like reliability function, hazard rate function, reverse hazard rate function, cumulant hazard rate function, mean waiting time, mean past life time, mean deviation, mean residual life function, second failure rate function for the proposed distribution. We also have derived different mathematical and statistical properties of this distribution including mean, variance, moment generating function, characteristic function, cumulant generating function, inverted moments, central moments, incomplete moments, conditional moments, probability weighted moments, order statistics, generalized entropy, Lorenz and Bonferroni curve and Zenga index. Parameter estimation using the maximum likelihood estimation method for the proposed distribution. Finally, we have demonstrated the suitability of the proposed model using two real data sets. [ABSTRACT FROM AUTHOR]

The paper focuses on type II Topp-Leone Frechet distribution. Its properties including hazard rate function, reverse hazard rate function, Mills ratio, quantile function and order statistics have been studied. The maximum likelihood estimation used for estimating the parameters of the proposed distribution has been explained and expressions for the Fisher information matrix and confidence intervals have been provided. The paper discusses the applications of the distribution for modeling several datasets relating to temperature. Finally, the goodness of fit of the proposed distribution has been compared with that of the Frechet distribution. [ABSTRACT FROM AUTHOR]

This paper presents a new Marshall-Olkin extended family of distributions with bounded support. Some of the Mathematical properties of the proposed distribution were studied and the method of maximum likelihood estimation was employed to estimate the unknown parameters of the proposed distribution. A Monte Carlo simulation study was carried out to examine the asymptotic behaviour of the parameter estimates of the distribution.” Finally, two real data sets defined on a unit interval were used to show the applicability of the proposed distribution in analyzing real data sets. [ABSTRACT FROM AUTHOR]

In this paper, the statistical inference of the lifetime performance index for the first failure progressive censoring schemes for the Topp Leone Alpha power exponential distribution (TLAPE) which excluded from a new structure of distribution models called T-Alpha Power X (T-APX) family is introduced. The proposed statistical inference of the lifetime performance index is applied on the High-Performance Liquid Chromatography data of blood samples from organ transplant recipients which is known as HPLC. The goodness of fit criteria of TLAPE for HPLC data proved the potentiality of TLAPE compared with other well-known distributions. This result has an effect on achieving the required results in testing procedure of the Lifetime performance index. Moreover, the statistical and reliability characteristics of TLAPE are studied. A simulation study is performed to examine the performance of the ML parameter estimates in terms of bias and mean square error. Two real data sets for survival and breast cancer are modeled using the TLAPE distribution and compared with other well-known distributions, to illustrate its performance. The results emphasize that the TLAPE distribution has a superior fitting performance to cancer data than the compared distributions. [ABSTRACT FROM AUTHOR]

The paper develops Bayesian estimators and credible intervals for the reliability function and hazard rate function of Topp-Leone distribution under Type-II censored data by considering informative prior and non-informative prior using symmetric and asymmetric loss functions. Further, Monte Carlo simulation study is carried out to find the Bayes estimates for reliability function and hazard rate along with their credible intervals. Real life data set is also taken up for illustration purpose. Robustness of hyper-parameters is also discussed. [ABSTRACT FROM AUTHOR]

In this article, a four parameter lifetime model called the Topp–Leone modified Weibull distribution is proposed. The suggested distribution can be considered as an alternative to Kumaraswamy Weibull, generalized modified Weibull, extend odd Weibull Lomax, Weibull-Lomax, Marshall-Olkin alpha power extended Weibull and exponentiated generalized alpha power exponential distributions, etc. The suggested model includes the Topp-Leone Weibull, Topp-Leone Linear failure rate, Topp-Leone exponential and Topp-Leone Rayleigh distributions as a special case. Several characteristics of the new suggested model including quantile function, moments, moment generating function, central moments, mean, variance, coefficient of skewness, coefficient of kurtosis, incomplete moments, the mean residual life and the mean inactive time are derived. The probability density function of the Topp–Leone modified Weibull distribution can be right skewed and uni-modal shaped but, the hazard rate function may be decreasing, increasing, J-shaped, U-shaped and bathtub on its parameters. Three different methods of estimation as; maximum likelihood, maximum product spacing and Bayesian methods are used to estimate the model parameters. For illustrative reasons, applications of the Topp–Leone modified Weibull model to four real data sets related to medical and engineering sciences are provided and contrasted with the fit reached by several other well-known distributions.

We developed a new generalized distribution referred to as the Topp-Leone Odd Exponential Half Logistic-G (TL-OEHL-G) distribution. The proposed distribution is an infinite linear combination of the exponentiated-G distribution. Some special cases from the TL-OEHL-G distribution are presented. The special cases of the TL-OEHL-G distribution apply to high skewed data and different forms of the hazard rate. Simulation study results for a selected special case are presented. Real data examples to demonstrate flexibility of the new model compared to other models are also provided. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper addresses estimation of the shape parameter of the Topp-Leone distribution which is known for its applicability in lifetime data. For fixed scale parameter, four plug-in estimators are suggested to estimate the shape parameter. The properties of these estimators are examined and their performances against the maximum likelihood estimator (MLE) are evaluated for a range of the shape parameter values. Based on the second moment, an estimator, which has an algebraic solution, is derived. It turns out that this proposed estimator outperforms the estimator based on the first moment that has no algebraic solution. A plug-in estimator based on solving the estimation equation mapping the empirical joint distribution function to the joint distribution function of a random sample is also derived and proven to constantly outperform the maximum likelihood estimator for all values of the shape parameter. [ABSTRACT FROM AUTHOR]

A new Topp–Leone generated family of distributions, which we call the Topp–Leone Discrete Laplace () distribution, is proposed. It has a shape parameter and a scale parameter . The is an alternative distribution for discrete data that have an asymmetric distribution. Some mathematical properties of the proposed distribution are also derived. Namely, we present the quantile function and the moments for the distribution. The Maximum Likelihood procedure is applied for parameter estimation. An application study is presented using real data. We use two data sets for this part of the analysis to illustrate the applications of the distribution. For the first data set, the change of the stock price in comparison with the closing price for the previous day is considered. The second data set provides information about the comparison of production cycle times of employees before and after the improvement a slippery production line in the degreasing alkaline process by increasing the pressure of the nozzle. The distribution is applied to a real life data and it fits data more efficiently than the Discrete Laplace () and Discrete Normal () distributions. [ABSTRACT FROM AUTHOR]

Statistical distributions are very useful in describing and predicting real world phenomena. Consequently, the choice of the most suitable statistical distribution for modeling given data is very important. In this paper, we propose a new class of lifetime distributions called the Weibull Topp-Leone Generated (WTLG) family. The proposed family is constructed via compounding the Weibull and the Topp-Leone distributions. It can provide better fits and is very flexible in comparison with the various known lifetime distributions. Several general statistical properties of the WTLG family are studied in details including density and hazard shapes, limit behavior, mixture representation, skewness and kurtosis, moments, moment generating function, incomplete moment. Different methods have been used to estimate its parameters. The performances of the estimators are numerically investigated. We have discussed inference on the new family based on the likelihood ratio statistics for testing some lifetime distributions. We assess the performance of the maximum likelihood estimators in terms of the biases and mean squared errors by means of a simulation study. The importance and flexibility of the new family are illustrated by means of two applications to real data sets. [ABSTRACT FROM AUTHOR]

The Topp-Leone distribution is an attractive model for life testing and reliability studies as it acquires a bathtub shaped hazard function. In this paper, we introduce a new family of distributions, depending on Topp- Leone random variable as a generator, called the Type II generalized Topp- Leone-G (TIIGTL-G) family. Its density function can be unimodel, leftskewed, right-skewed, and reversed-J shaped, and has increasing, decreasing, upside-down, J and reversed-J hazard rates. Some special models are presented. Some of its statistical properties are studied. Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Rényi entropy and order statistics are derived. The method of maximum likelihood is used to estimate the model parameters. The importance of one special model; namely; the Type II generalized Topp-Leone exponential is illustrated through two real data sets. [ABSTRACT FROM AUTHOR]

In this paper, we consider the estimation reliability in multicomponent stress-strength (MSS) model when both the stress and strengths are drawn from Topp-Leone (TL) distribution. The maximum likelihood (ML) and Bayesian methods are used in the estimation procedure. Bayesian estimates are obtained by using Lindley's approximation and Gibbs sampling methods, since they cannot be obtained in explicit form in the context of TL. The asymptotic confidence intervals are constructed based on the ML estimators. The Bayesian credible intervals are also constructed using Gibbs sampling. The reliability estimates are compared via an extensive Monte-Carlo simulation study. Finally, a real data set is analysed for illustrative purposes. [ABSTRACT FROM AUTHOR]

A new family of distributions called the Topp-Leone generalized odd log-logistic-G family is introduced and studied. We provide some mathematical properties of the new family including ordinary and incomplete moments, generating function and order statistics. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of two simulation studies. Finally, the usefulness of the family is illustrated by means of two real data sets. The new model provides consistently better fits than other competitive models for these data sets. [ABSTRACT FROM AUTHOR]

In this paper, we have derived exact and explicit expressions for the ratio and inverse moments of dual generalized order statistics from Topp-Leone distribution. This result includes the single and product moments of order statistics and lower records. Further, based on n dual generalized order statistics, we have deduced the expression for Maximum likelihood estimator (MLE) and Uniformly minimum variance unbiased estimator (UMVUE) for the shape parameter of Topp-Leone distribution. Finally, based on order statistics and lower records, a simulation study is being carried out to check the efficiency of these estimators. [ABSTRACT FROM AUTHOR]

In this article, a new three parameters lifetime model called the Topp-Leone Generalized Inverted Exponential (TLGIE) Distribution is introduced. Various properties of the model are derived, including moments, quantile function, survival function, hazard rate function, mean deviation and mode. The method of maximum likelihood is used to estimate the unknown parameters. The properties of the maximum likelihood estimators using Fisher information matrix are studied. Three real data sets are applied for illustrative purpose of this study.

In this paper, Topp-Leone Mukherjee-Islam (TLMI) distribution is suggested. The probability density function and the distribution function of the TLMI are provided. The rth moment, mean, variance, coefficient of skewness, kurtosis, and coefficient of variation are derived. The order statistics of the TLMI distribution random variable are introduced. Reliability analysis including the hazard rate function reliability function are studied. The maximum likelihood estimators of the TLMI distribution parameters and the Rényi entropy as a measure of the uncertainty in the model are obtained. The usefulness of the TLMI distribution is illustrated using real lifetime data set from medical science. [ABSTRACT FROM AUTHOR]

In this paper, we study inference for the stress-strength reliability based on lower record data, where the stress and the strength variables are modeled by two independent but not identically distributed random variables from distributions belonging to the proportional reversed hazard family. Likelihood and Bayesian estimators are derived, then confidence intervals and credible sets are obtained. Moreover, we consider the Topp-Leone distribution as a particular case of distribution belonging to this family and we derive some numerical results in order to show the performance of the proposed procedures. Finally, two applications to real data are reported. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new generalized family of distributions from bounded support (0,1), namely, the Topp-Leone-G family. Some of mathematical properties of the proposed family have been studied. The new density function can be symmetrical, left-skewed, right-skewed or reverse-J shaped. Furthermore, the hazard rate function can be constant, increasing, decreasing, J or bathtub hazard rate shapes. Three special models are discussed. We obtain simple expressions for the ordinary and incomplete moments, quantile and generating functions, mean deviations and entropies. The method of maximum likelihood is used to estimate the model parameters. The flexibility of the new family is illustrated by means of three real data sets. [ABSTRACT FROM AUTHOR]

In this study, we propose a new flexible two-parameter continuous distribution with support on the unit interval. It can be identified as a special member of the so-called type I half-logistic-G family of distributions, defined with the Topp−Leone distribution as baseline. Among its features, the corresponding probability density function can be left skewed, right-skewed, approximately symmetric, J-shaped, as well as reverse J-shaped, making it suitable for modeling a wide variety of data sets. It thus provides an alternative to the so-called beta and Kumaraswamy distributions. The mathematical properties of the new distribution are determined, deriving the asymptotes, shapes, quantile function, skewness, kurtosis, some power series expansions, ordinary moments, incomplete moments, moment-generating function, stress strength parameter, and order statistics. Then, a statistical treatment of the related model is proposed. The estimation of the unknown parameters is performed by a simulation study exploring seven methods, all described in detail. Two practical data sets are analyzed, showing the usefulness of the new proposed model.

We introduce a new class of continuous distributions named the Topp–Leone odd log-logistic family, which extends the one-parameter distribution pioneered by Topp and Leone [A family of J-shaped frequency functions. J Amer Statist Assoc. 1955;50:209–219]. We study some of its mathematical properties and describe two special cases. Further, we propose a regression model based on the new Topp–Leone odd log-logistic Weibull distribution. The usefulness and flexibility of the proposed family are illustrated by means of three real data sets. [ABSTRACT FROM PUBLISHER]

In this paper, a new class of lifetime distribution, which is called Topp-Leone (J-shaped) geometric distribution, is obtained by compound of the Topp-Leone and geometric distributions. Reliability and statistical properties of the new distribution such as quantiles, moment, hazard rate, reversed hazard rate, mean residual life, mean inactivity time, entropies, moment generating function, order statistics and their stochastic orderings are obtained. Estimation of the model parameters by least squares, weighted least squares, maximum likelihood and the observed information matrix are derived. Finally, a real data set is analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this study, we construct a continuous probability distribution as an improvement of Topp-Leone distribution. However, density function and the cumulative function of the constructed distribution (Burr X-Topp Leone distribution) were obtained. Also, we show the validity of the new distribution. [ABSTRACT FROM AUTHOR]

We consider the estimation problem of the probabilityP=P(X>Y) for the standard Topp–Leone distribution. After discussing the maximum likelihood and uniformly minimum variance unbiased estimation procedures for the problem on both complete and left censored samples, we perform a Monte Carlo simulation to compare the estimators based on the mean square error criteria. We also consider the interval estimation ofP. [ABSTRACT FROM AUTHOR]

We derive explicit algebraic expressions for both of the single and product moments of order statistics from Topp-Leone distribution. We also give an identity about single moments of order statistics. These expressions will be useful for computational purposes. [ABSTRACT FROM AUTHOR]