TOPP LEONE WEIBULL LOMAX DISTRIBUTION: PROPERTIES, REGRESSION MODEL AND APPLICATIONS

A new four-parameter lifetime distribution (called the Topp Leone Weibull-Lomax distribution) is proposed in this paper. Different mathematical properties of the proposed distribution were studied which include quantile function, ordinary and incomplete moments, probability weighted moment, conditional moments, order statistics, stochastic ordering, and stress-strength reliability parameter. The regression model and the residual analysis for the proposed model were also carried out. The model parameters were estimated by using the maximum likelihood criterion and the behaviour of these estimated parameters were examined by conducting a simulation study. The importance and flexibility of the proposed distribution have been proved empirically by using four separate data sets.

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EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

NED University Journal of Research ◽

10.35453/nedjr-ascn-2018-0033 ◽

2019 ◽

Vol XVI (2) ◽

pp. 1-11

Author(s):

Farrukh Jamal ◽

Hesham Mohammed Reyad ◽

Soha Othman Ahmed ◽

Muhammad Akbar Ali Shah ◽

Emrah Altun

Keyword(s):

Real Data ◽

Continuous Model ◽

Model Parameters ◽

Data Set ◽

Lomax Distribution ◽

Mathematical Properties ◽

Proposed Model ◽

Probability Weighted Moment ◽

Record Statistics ◽

Maximum Likelihood Criterion

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.

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A New Generalized Weighted Weibull Distribution

Pakistan Journal of Statistics and Operation Research ◽

10.18187/pjsor.v15i1.2782 ◽

2019 ◽

pp. 161-178 ◽

Cited By ~ 1

Author(s):

Salman Abbas ◽

Gamze Ozal ◽

Saman Hanif Shahbaz ◽

Muhammad Qaiser Shahbaz

Keyword(s):

Weibull Distribution ◽

Generating Function ◽

Probability Generating Function ◽

Real Data ◽

Quantile Function ◽

Moment Generating Function ◽

Likelihood Method ◽

Model Parameters ◽

Data Sets ◽

Proposed Model

In this article, we present a new generalization of weighted Weibull distribution using Topp Leone family of distributions. We have studied some statistical properties of the proposed distribution including quantile function, moment generating function, probability generating function, raw moments, incomplete moments, probability, weighted moments, Rayeni and q th entropy. The have obtained numerical values of the various measures to see the eect of model parameters. Distribution of of order statistics for the proposed model has also been obtained. The estimation of the model parameters has been done by using maximum likelihood method. The eectiveness of proposed model is analyzed by means of a real data sets. Finally, some concluding remarks are given.

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Beta Kumaraswamy Burr Type X Distribution and Its Properties

10.20944/preprints201808.0304.v1 ◽

2018 ◽

Author(s):

Umar Yusuf Madaki ◽

Mohd Rizam Abu Bakar ◽

Laba Handique

Keyword(s):

Maximum Likelihood ◽

Reliability Analysis ◽

Real Data ◽

Quantile Function ◽

Model Parameters ◽

Data Sets ◽

Likelihood Methods ◽

Proposed Model ◽

Maximum Likelihood Methods ◽

True Values

We proposed a so-called Beta Kumaraswamy Burr Type X distribution which gives the extension of the Kumaraswamy-G class of family distribution. Some properties of this proposed model were provided, like: the expansion of densities and quantile function. We considered the Bayes and maximum likelihood methods to estimate the parameters and also simulate the model parameters to validate the methods based on different set of true values. Some real data sets were employed to show the usefulness and flexibility of the model which serves as generalization to many sub-models in the field of engineering, medical, survival and reliability analysis.

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Beta Kumaraswamy Burr Type X Distribution and Its Properties

10.20944/preprints201808.0356.v1 ◽

2018 ◽

Author(s):

Umar Yusuf Madaki ◽

Mohd Rizam Abu Bakar ◽

Laba Handique

Keyword(s):

Maximum Likelihood ◽

Reliability Analysis ◽

Real Data ◽

Quantile Function ◽

Model Parameters ◽

Data Sets ◽

Likelihood Methods ◽

Proposed Model ◽

Maximum Likelihood Methods ◽

True Values

We proposed a so-called Beta Kumaraswamy Burr Type X distribution which gives the extension of the Kumaraswamy-G class of family distribution. Some properties of this proposed model were provided, like: the expansion of densi- ties and quantile function. We considered the Bayes and maximum likelihood methods to estimate the parameters and also simulate the model parameters to validate the methods based on dierent set of true values. Some real data sets were employed to show the usefulness and  exibility of the model which serves as generalization to many sub-models in the elds of engineering, medical, survival and reliability analysis.

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

Symmetry ◽

10.3390/sym12010075 ◽

2020 ◽

Vol 12 (1) ◽

pp. 75 ◽

Cited By ~ 3

Author(s):

Rashad A. R. Bantan ◽

Farrukh Jamal ◽

Christophe Chesneau ◽

Mohammed Elgarhy

Keyword(s):

Natural Extension ◽

Stochastic Ordering ◽

Quantile Function ◽

Model Parameters ◽

Data Sets ◽

Type Ii ◽

New Family ◽

The Family ◽

Family Based ◽

High Level

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.

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Theory and Applications of the Unit Gamma/Gompertz Distribution

Mathematics ◽

10.3390/math9161850 ◽

2021 ◽

Vol 9 (16) ◽

pp. 1850

Author(s):

Rashad A. R. Bantan ◽

Farrukh Jamal ◽

Christophe Chesneau ◽

Mohammed Elgarhy

Keyword(s):

Stochastic Ordering ◽

Real Data ◽

Rate Function ◽

The Other ◽

Likelihood Method ◽

Model Parameters ◽

Data Sets ◽

Gompertz Distribution ◽

Probability And Statistics ◽

Analytical Behavior

Unit distributions are commonly used in probability and statistics to describe useful quantities with values between 0 and 1, such as proportions, probabilities, and percentages. Some unit distributions are defined in a natural analytical manner, and the others are derived through the transformation of an existing distribution defined in a greater domain. In this article, we introduce the unit gamma/Gompertz distribution, founded on the inverse-exponential scheme and the gamma/Gompertz distribution. The gamma/Gompertz distribution is known to be a very flexible three-parameter lifetime distribution, and we aim to transpose this flexibility to the unit interval. First, we check this aspect with the analytical behavior of the primary functions. It is shown that the probability density function can be increasing, decreasing, “increasing-decreasing” and “decreasing-increasing”, with pliant asymmetric properties. On the other hand, the hazard rate function has monotonically increasing, decreasing, or constant shapes. We complete the theoretical part with some propositions on stochastic ordering, moments, quantiles, and the reliability coefficient. Practically, to estimate the model parameters from unit data, the maximum likelihood method is used. We present some simulation results to evaluate this method. Two applications using real data sets, one on trade shares and the other on flood levels, demonstrate the importance of the new model when compared to other unit models.

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An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

Mathematica Slovaca ◽

10.1515/ms-2017-0406 ◽

2020 ◽

Vol 70 (4) ◽

pp. 953-978

Author(s):

Mustafa Ç. Korkmaz ◽

G. G. Hamedani

Keyword(s):

Hazard Function ◽

Mixture Distribution ◽

Real Data ◽

Quantile Function ◽

Estimation Methods ◽

Data Sets ◽

Unknown Parameters ◽

Lorenz Curves ◽

Proposed Model ◽

New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

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The Weibull Birnbaum-Saunders Distribution And Its Applications

Statistics Optimization & Information Computing ◽

10.19139/soic-2310-5070-887 ◽

2020 ◽

Vol 9 (1) ◽

pp. 61-81

Author(s):

Lazhar BENKHELIFA

Keyword(s):

Maximum Likelihood ◽

Estimation Method ◽

Likelihood Estimation ◽

Real Data ◽

Reliability Estimation ◽

Maximum Likelihood Estimates ◽

Model Parameters ◽

Data Sets ◽

Proposed Model ◽

Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

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An Alternate Generalized Odd Generalized Exponential Family with Applications to Premium Data

Symmetry ◽

10.3390/sym13112064 ◽

2021 ◽

Vol 13 (11) ◽

pp. 2064

Author(s):

Sadaf Khan ◽

Oluwafemi Samson Balogun ◽

Muhammad Hussain Tahir ◽

Waleed Almutiry ◽

Amani Abdullah Alahmadi

Keyword(s):

Exponential Family ◽

Simulation Analysis ◽

Structural Characteristics ◽

Stochastic Ordering ◽

Quantile Function ◽

Risk Theory ◽

Data Sets ◽

Exponential Distributions ◽

New Family ◽

Lehmann Alternative

In this article, we use Lehmann alternative-II to extend the odd generalized exponential family. The uniqueness of this family lies in the fact that this transformation has resulted in a multitude of inverted distribution families with important applications in actuarial field. We can characterize the density of the new family as a linear combination of generalised exponential distributions, which is useful for studying some of the family’s properties. Among the structural characteristics of this family that are being identified are explicit expressions for numerous types of moments, the quantile function, stress-strength reliability, generating function, Rényi entropy, stochastic ordering, and order statistics. The maximum likelihood methodology is often used to compute the new family’s parameters. To confirm that our results are converging with reduced mean square error and biases, we perform a simulation analysis of one of the special model, namely OGE2-Fréchet. Furthermore, its application using two actuarial data sets is achieved, favoring its superiority over other competitive models, especially in risk theory.

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Statistical Inference of the Half-Logistic Inverse Rayleigh Distribution

Entropy ◽

10.3390/e22040449 ◽

2020 ◽

Vol 22 (4) ◽

pp. 449 ◽

Cited By ~ 2

Author(s):

Abdullah M. Almarashi ◽

Majdah M. Badr ◽

Mohammed Elgarhy ◽

Farrukh Jamal ◽

Christophe Chesneau

Keyword(s):

Statistical Inference ◽

Goodness Of Fit ◽

Stochastic Ordering ◽

Linear Representation ◽

Rayleigh Distribution ◽

Model Parameters ◽

Data Sets ◽

New Model ◽

Entropy Measures ◽

Lifetime Studies

The inverse Rayleigh distribution finds applications in many lifetime studies, but has not enough overall flexibility to model lifetime phenomena where moderately right-skewed or near symmetrical data are observed. This paper proposes a solution by introducing a new two-parameter extension of this distribution through the use of the half-logistic transformation. The first contribution is theoretical: we provide a comprehensive account of its mathematical properties, specifically stochastic ordering results, a general linear representation for the exponentiated probability density function, raw/inverted moments, incomplete moments, skewness, kurtosis, and entropy measures. Evidences show that the related model can accommodate the treatment of lifetime data with different right-skewed features, so far beyond the possibility of the former inverse Rayleigh model. We illustrate this aspect by exploring the statistical inference of the new model. Five classical different methods for the estimation of the model parameters are employed, with a simulation study comparing the numerical behavior of the different estimates. The estimation of entropy measures is also discussed numerically. Finally, two practical data sets are used as application to attest of the usefulness of the new model, with favorable goodness-of-fit results in comparison to three recent extended inverse Rayleigh models.

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