The Topp–Leone odd log-logistic family of distributions

A New Extension of the Topp-Leone-Family of Models with Applications to Real Data

In this article, we proposed a new extension of the Topp-Leone family of distributions. Some important properties of the model are developed, such as quantile function, stochastic ordering, model series representation, moments, stress-strength reliability parameter, Renyi entropy, order statistics, and moment of residual life. A particular member called new extended Topp-Leone exponential (NETLE) is discussed. Maximum likelihood estimation (MLE), least-square estimation (LSE), and percentile estimation (PE) are used for the model parameter estimation. Simulation studies were conducted using NETLE to assess the MLE, LSE, and PE performance by examining their bias and mean square error (MSE), and the result was satisfactory. Finally, the applications of the NETLE to two real data sets are provided to illustrate the importance of the NETLG families in practice; the data sets consist of daily new deaths due to COVID-19 in California and New Jersey, USA. The new model outperformed many other existing Topp-Leone's and exponential related distributions based on the real data illustrations.

A new lifetime family of distributions: Theoretical developments and analysis of COVID 19 data

In parametric statistical modeling and inference, it is critical to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets. Thus , this paper contributes to the subject by investigating a new flexible and versatile generalized family of distributions defined from the alliance of the families known as beta-G and Topp-Leone generated (TL-G), inspiring the name of BTL-G family. The characteristics of this new family are studied through analytical, graphical and numerical approaches. Statistical features of the family such as expansion of density function (pdf), cumulative function (cdf), moments (MOs), incomplete moments (IMOs), mean deviation (MDE), and entropy (ENT) are calculated. The model parameters' maximum likelihood estimates (MaxLEs) and Bayesian estimates (BEs) are provided. Symmetric and Asymmetric Bayesian Loss function have been discussed. A complete simulation study is proposed to illustrate their numerical efficiency. The considered model is also applied to analyze two different kinds of genuine COVID 19 data sets. We show that it outperforms other well-known models defined with the same baseline distribution, proving its high level of adaptability in the context of data analysis.

Topp-Leone odd log-logistic exponential distribution: Its improved estimators and applications

In this paper, a new three-parameter lifetime model called the Topp-Leone odd log-logistic exponential distribution is proposed. Its density function can be expressed as a linear mixture of exponentiated exponential densities and can be reversed-J shaped, skewed to the left and to the right. Further, the hazard rate function of the new model can be monotone, unimodal, constant, J-shaped, constant-increasing-decreasing and decreasing-increasing-decreasing and bathtub-shaped. Our main focus is on estimation from a frequentist point of view, yet, some statistical and reliability characteristics for the proposed model are derived. We briefly describe different estimators namely, the maximum likelihood estimators, ordinary least-squares estimators, weighted least-squares estimators, percentile estimators, maximum product of spacings estimators, Cramér-von-Mises minimum distance estimators, Anderson-Darling estimators and right-tail Anderson-Darling estimators. Monte Carlo simulations are performed to compare the performance of the proposed methods of estimation for both small and large samples. We illustrate the performance of the proposed distribution by means of two real data sets and both the data sets show the new distribution is more appropriate as compared to some other well-known distributions.

A New Flexible Family of Continuous Distributions: The Additive Odd-G Family

This paper introduces a new family of distributions based on the additive model structure. Three submodels of the proposed family are studied in detail. Two simulation studies were performed to discuss the maximum likelihood estimators of the model parameters. The log location-scale regression model based on a new generalization of the Weibull distribution is introduced. Three datasets were used to show the importance of the proposed family. Based on the empirical results, we concluded that the proposed family is quite competitive compared to other models.

Evaluation of the lifetime performance index on first failure progressive censored data based on Topp Leone Alpha power exponential model applied on HPLC data

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.

The Burr III-Topp-Leone-G family of distributions with applications

In this article, we present a new family of generalized distributions called the Burr III-Topp-Leone-G (BIII-TL-G). We further study in detail its structural properties including moments, probability weighted moments, distribution of order statistics, and entropy. The maximum likelihood estimation method is used to estimate the model parameters. Simulations are carried out to show the consistency and efficiency of parameter estimates and finally, real data sets are used to demonstrate the applicability of the proposed model.

Comparison between Highly Complex Location Models and GAMLSS

This paper presents a discussion regarding regression models, especially those belonging to the location class. Our main motivation is that, with simple distributions having simple interpretations, in some cases, one gets better results than the ones obtained with overly complex distributions. For instance, with the reverse Gumbel (RG) distribution, it is possible to explain response variables by making use of the generalized additive models for location, scale, and shape (GAMLSS) framework, which allows the fitting of several parameters (characteristics) of the probabilistic distributions, like mean, mode, variance, and others. Three real data applications are used to compare several location models against the RG under the GAMLSS framework. The intention is to show that the use of a simple distribution (e.g., RG) based on a more sophisticated regression structure may be preferable than using a more complex location model.

On A New Two Parameter Fréchet Distribution with Applications

A new ‡exible extension of the Fréchet model is proposed and studied. Some of itsfundamental statistical properties are derived. The importance of the new model is shown via two applications to real data sets. A simple type Copula based construction are also presented.We assess the performance of the maximum likelihood estimations of the new distribution with respect to sample size n. The assessment was based on a simulation study.The new model is much better than other important competitive models.

Right Truncated of Mixture Topp-Leone with Exponential Distribution

In this paper the truncated distribution from the right was found for our distribution resulting from the mixing of two Topp Leone with the exponential distributions. The CDF and PDF are derived, as are the survival, moment and hazard functions. Two methods for estimating the parameters were derived, namely the maximum likelihood method and the moment method, as well as in the data analysis an algorithm was constructed and applied in the MATLAB.

A New Bimodal Distribution for Modeling Asymmetric Bimodal Heavy-Tail Real Lifetime Data

We introduced and studied a new generalization of the Burr type X distribution. Some of its properties were derived and numerically analyzed. The new density can be “right-skewed” and symmetric with “unimodal” and many “bimodal” shapes. The new failure rate can be “increasing,” “bathtub,” “J-shape,” “decreasing,” “increasing-constant-increasing,” “reversed J-shape,” and “upside-down (reversed U-shape).” The usefulness and flexibility of the new distribution were illustrated by means of four asymmetric bimodal right- and left-heavy tail real lifetime data.

Type II Power Topp-Leone Generated Family of Distributions with Statistical Inference and Applications

In this paper, we present and study a new family of continuous distributions, called the type II power Topp-Leone-G family. It provides a natural extension of the so-called type II Topp-Leone-G family, thanks to the use of an additional shape parameter. We determine the main properties of the new family, showing how they depend on the involving parameters. The following points are investigated: shapes and asymptotes of some important functions, quantile function, some mixture representations, moments and derivations, stochastic ordering, reliability and order statistics. Then, a special model of the family based on the inverse exponential distribution is introduced. It is of particular interest because the related probability functions are tractable and possess various kinds of asymmetric shapes. Specially, reverse J, left skewed, near symmetrical and right skewed shapes are observed for the corresponding probability density function. The estimation of the model parameters is performed by the use of three different methods. A complete simulation study is proposed to illustrate their numerical efficiency. The considered model is also applied to analyze two different kinds of data sets. We show that it outperforms other well-known models defined with the same baseline distribution, proving its high level of adaptability in the context of data analysis.

Extended Odd Fréchet-G Family of Distributions

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.