scholarly journals The McDonald Lindley-Poisson Distribution

2021 ◽  
pp. 1095-1112
Author(s):  
Ana Percontini ◽  
Ronaldo V. da Silva ◽  
Laba Handique ◽  
Pedro Rafael Diniz Marinho
Keyword(s):  
Data Analysis ◽  
Poisson Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Lifetime Data ◽  
Mathematical Properties ◽  
Lifetime Data Analysis ◽  
New Distribution ◽  
Flexible Model

We propose the McDonald Lindley-Poisson distribution and derive some of its mathematical properties including explicit expressions for moments, generating and quantile functions, mean deviations, order statistics and their moments. Its model parameters are estimated by maximum likelihood. A simulation study investigates the performance of the estimates. The new distribution represents a more flexible model for lifetime data analysis than other existing models as proved empirically by means of two real data sets.

scholarly journals A New Burr XII-Weibull-Logarithmic Distribution for Survival and Lifetime Data Analysis: Model, Theory and Applications

Stats ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 77-91
Author(s):  
Broderick Oluyede ◽  
Boikanyo Makubate ◽  
Adeniyi Fagbamigbe ◽  
Precious Mdlongwa
Keyword(s):  
Likelihood Estimation ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Analysis Model ◽  
Conditional Moments ◽  
Compound Distribution ◽  
Lifetime Data Analysis ◽  
Logarithmic Distribution ◽  
New Distribution

A new compound distribution called Burr XII-Weibull-Logarithmic (BWL) distribution is introduced and its properties are explored. This new distribution contains several new and well known sub-models, including Burr XII-Exponential-Logarithmic, Burr XII-Rayleigh-Logarithmic, Burr XII-Logarithmic, Lomax-Exponential-Logarithmic, Lomax–Rayleigh-Logarithmic, Weibull, Rayleigh, Lomax, Lomax-Logarithmic, Weibull-Logarithmic, Rayleigh-Logarithmic, and Exponential-Logarithmic distributions. Some statistical properties of the proposed distribution including moments and conditional moments are presented. Maximum likelihood estimation technique is used to estimate the model parameters. Finally, applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution.

scholarly journals The Weibull-G Poisson Family for Analyzing Lifetime Data

2020 ◽  
pp. 131-148 ◽  
Author(s):  
Haitham Yousof ◽  
Muhammad Mansoor ◽  
Morad Alizadeh ◽  
Ahmed Afify ◽  
Indranil Ghosh
Keyword(s):  
Generating Functions ◽  
Likelihood Estimation ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Lifetime Data ◽  
New Family ◽  
Mathematical Properties ◽  
Independent Identically Distributed ◽  
Family Of Distributions

We study a new family of distributions defined by the minimum of the Poissonrandom number of independent identically distributed random variables having a general Weibull-G distribution (see Bourguignon et al. (2014)). Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics, reliability and entropies are derived. Maximum likelihood estimation of the model parameters is investigated. Three special models of the new family are discussed. We perform three applications to real data sets to show the potentiality of theproposed family.

scholarly journals A New Generalized Family of Distributions for Lifetime Data

2021 ◽  
Vol 19 (1) ◽  
pp. 2-23
Author(s):  
Maha A. D. Aldahlan ◽  
Mohamed G. Khalil ◽  
Ahmed Z. Afify
Keyword(s):  
Generating Functions ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Lifetime Data ◽  
New Class ◽  
New Family ◽  
Mathematical Properties ◽  
Generated Family ◽  
Family Of Distributions

A new class of continuous distributions called the generalized Burr X-G family is introduced. Some special models of the new family are provided. Some of its mathematical properties including explicit expressions for the quantile and generating functions, ordinary and incomplete moments, order statistics and Rényi entropy are derived. The maximum likelihood is used for estimating the model parameters. The flexibility of the generated family is illustrated by means of two applications to real data sets.

scholarly journals The Complementary Exponentiated Lomax-Poisson Distribution with Applications to Bladder Cancer and Failure Data

2021 ◽  
Vol 50 (3) ◽  
pp. 77-105
Author(s):  
Devendra Kumar ◽  
Mazen Nassar ◽  
Ahmed Z. Afify ◽  
Sanku Dey
Keyword(s):  
Least Squares ◽  
Poisson Distribution ◽  
Weighted Least Squares ◽  
Real Data ◽  
Random Variable ◽  
Model Parameters ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
Failure Data ◽  
New Distribution

A new continuous four-parameter lifetime distribution is introduced by compounding the distribution of the maximum of a sequence of an independently identically exponentiated Lomax distributed random variables and zero truncated Poisson random variable, defined as the complementary exponentiated Lomax Poisson (CELP) distribution. The new distribution which exhibits decreasing and upside down bathtub shaped density while the distribution has the ability to model lifetime data with decreasing, increasing and upside-down bathtub shaped failure rates. The new distribution has a number of well-known lifetime special sub-models, such as Lomax-zero truncated Poisson distribution, exponentiated Pareto-zero truncated Poisson distribution and Pareto- zero truncated Poisson distribution. A comprehensive account of the mathematical and statistical properties of the new distribution is presented. The model parameters are obtained by the methods of maximum likelihood, least squares, weighted least squares, percentiles, maximum product of spacing and Cram\'er-von-Mises and compared them using Monte Carlo simulation study. 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 the transmuted Lomax, beta exponentiated Lomax, McDonald Lomax, Kumaraswamy Lomax, Weibull Lomax, Burr X Lomax and Lomax distributions.

scholarly journals A New Flexible Version of the Lomax Distribution with Applications

2018 ◽  
Vol 7 (5) ◽  
pp. 120
Author(s):  
T. H. M. Abouelmagd
Keyword(s):  
Estimation Method ◽  
Good Alternative ◽  
Model Parameters ◽  
Data Sets ◽  
Suitable Model ◽  
Lifetime Data ◽  
New Model ◽  
The Right ◽  
New Distribution ◽  
Better Than

A new version of the Lomax model is introduced andstudied. The major justification for the practicality of the new model isbased on the wider use of the Lomax model. We are also motivated tointroduce the new model since the density of the new distribution exhibitsvarious important shapes such as the unimodal, the right skewed and the leftskewed. The new model can be viewed as a mixture of the exponentiated Lomaxdistribution. It can also be considered as a suitable model for fitting thesymmetric, left skewed, right skewed, and unimodal data sets. The maximumlikelihood estimation method is used to estimate the model parameters. Weprove empirically the importance and flexibility of the new model inmodeling two types of aircraft windshield lifetime data sets. The proposedlifetime model is much better than gamma Lomax, exponentiated Lomax, Lomaxand beta Lomax models so the new distribution is a good alternative to thesemodels in modeling aircraft windshield data.

scholarly journals A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 440 ◽  
Author(s):  
Abdulhakim A. Al-babtain ◽  
I. Elbatal ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Simple Type ◽  
Data Sets ◽  
New Model ◽  
Clayton Copula ◽  
Mathematical Properties

In this article, we introduced a new extension of the binomial-exponential 2 distribution. We discussed some of its structural mathematical properties. A simple type Copula-based construction is also presented to construct the bivariate- and multivariate-type distributions. We estimated the model parameters via the maximum likelihood method. Finally, we illustrated the importance of the new model by the study of two real data applications to show the flexibility and potentiality of the new model in modeling skewed and symmetric data sets.

scholarly journals On Erlang-Truncated Exponential Distribution: Theory and Application

2021 ◽  
pp. 155-168
Author(s):  
Ibrahim Elbatal ◽  
A. Aldukeel
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Mean Deviation ◽  
Model Parameters ◽  
Data Sets ◽  
Survival Times ◽  
New Distribution ◽  
Better Than

In this article, we introduce a new distribution called the McDonald Erlangtruncated exponential distribution. Various structural properties including explicit expressions for the moments, moment generating function, mean deviation of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated by two real data sets. The new model is much better than other important competitive models in modeling relief times and survival times data sets.

scholarly journals The Gumbel- Pareto Distribution: Theory and Applications

2019 ◽  
Vol 16 (4) ◽  
pp. 0937
Author(s):  
Saad Et al.
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Numerical Illustration ◽  
Data Set ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
First Time ◽  
New Distribution

In this paper, for the first time we introduce a new four-parameter model called the Gumbel- Pareto distribution by using the T-X method. We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters. Numerical illustration and an application to a real data set are given to show the flexibility and potentiality of the new model.

scholarly journals The Transmuted Odd Lindley-G Family of Distributions

2018 ◽  
pp. 1-25 ◽  
Author(s):  
Hesham Reyad ◽  
Farrukh Jamal ◽  
Soha Othman ◽  
G. G. Hamedani
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Strength Model ◽  
New Family ◽  
Mathematical Properties ◽  
Probability Weighted Moments ◽  
Family Of Distributions

We propose a new generator of univariate continuous distributions with two extra parameters called the transmuted odd-Lindley generator which extends the odd Lindely-G family introduced by Gomes-Silva et al. [1]. Some mathematical properties of the new generator such as, the ordinary and incomplete moments, generating function, stress strength model, Rényi entropy, probability weighted moments and order statistics are investigated. Certain characterisations of the proposed family are estimated. We discuss the maximum likelihood estimates and the observed information matrix for the model parameters. The potentiality of the new family is illustrated by means of five applications to real data sets.  

scholarly journals The Weighted Power Lindley Distribution with Applications on the Life Time Data

2020 ◽  
pp. 225-237
Author(s):  
Aafaq A. Rather ◽  
Gamze Özel
Keyword(s):  
Information Matrix ◽  
Life Time ◽  
Real Data ◽  
Data Sets ◽  
Lifetime Data ◽  
Time Data ◽  
Data Set ◽  
Lindley Distribution ◽  
Power Lindley Distribution ◽  
New Distribution

In this paper, we have proposed a new version of power lindley distribution known as weighted power lindley distribution. The different structural properties of the newly model have been studied. The maximum likelihood estimators of the parameters and the Fishers information matrix have been discussed. It also provides more flexibility to analyze complex real data sets.  An application of the model to a real data set is analyzed using the new distribution, which shows that the weighted power Lindley distribution can be used quite effectively in analyzing real lifetime data.

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