scholarly journals On The Burr XII-Gamma Distribution: Development, Properties, Characterizations and Applications

2021 ◽  
pp. 771-789
Author(s):  
Fiaz Ahmad Bhatti ◽  
Gauss M. Cordeiro ◽  
Mustafa Ç. Korkmaz ◽  
G.G. Hamedani
Keyword(s):  
Random Number Generator ◽  
Likelihood Estimation ◽  
Real Data ◽  
Record Values ◽  
Rate Function ◽  
Data Sets ◽  
Failure Rate Function ◽  
Conditional Moments ◽  
Mathematical Properties ◽  
Proposed Model

We introduce a four-parameter lifetime model with flexible hazard rate called the Burr XII gamma (BXIIG) distribution.  We derive the BXIIG distribution from (i) the T-X family technique and (ii) nexus between the exponential and gamma variables. The failure rate function for the BXIIG distribution is flexible as it can accommodate various shapes such as increasing, decreasing, decreasing-increasing, increasing-decreasing-increasing, bathtub and modified bathtub.  Its density function can take shapes such as exponential, J, reverse-J, left-skewed, right-skewed and symmetrical. To illustrate the importance of the BXIIG distribution, we establish various mathematical properties such as random number generator, ordinary moments, generating function, conditional moments, density functions of record values, reliability measures and characterizations.  We address the maximum likelihood estimation for the parameters. We estimate the adequacy of the estimators via a simulation study. We consider applications to two real data sets to prove empirically the potentiality of the proposed model.

Extended exponentiated Nadarajah-Haghighi model: Mathematical properties, characterizations and applications

2018 ◽  
Vol 55 (4) ◽  
pp. 498-522
Author(s):  
Morad Alizadeh ◽  
Mahdi Rasekhi ◽  
Haitham M. Yousof ◽  
Thiago G. Ramires ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Survival Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Rate Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Failure Rate Function ◽  
Data Set ◽  
Mathematical Properties

In this article, a new four-parameter model is introduced which can be used in mod- eling survival data and fatigue life studies. Its failure rate function can be increasing, decreasing, upside down and bathtub-shaped depending on its parameters. We derive explicit expressions for some of its statistical and mathematical quantities. Some useful characterizations are presented. Maximum likelihood method is used to estimate the model parameters. The censored maximum likelihood estimation is presented in the general case of the multi-censored data. We demonstrate empirically the importance and exibility of the new model in modeling a real data set.

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

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.

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 Ristic-Balakrishnan odd log-logistic family of distributions: Properties and Applications

2020 ◽  
Vol 8 (1) ◽  
pp. 17-35
Author(s):  
Hamid Esmaeili ◽  
Fazlollah Lak ◽  
Emrah Altun
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Model Parameters ◽  
Mathematical Properties ◽  
Proposed Model ◽  
The Family ◽  
Logistic Family ◽  
Family Of Distributions ◽  
Extra Parameter

This paper investigates general mathematical properties of a new generator of continuous distributions with two extra parameter called the Ristic-Balakrishnan odd log-logistic family of distributions. We present some special models and investigate the asymptotes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Explicit expressions for the ordinary and incomplete moments, generating functions and order statistics, which hold for any baseline model, are determined. Further, we discuss the estimation of the model parameters by maximum likelihood and present a simulation study based on maximum likelihood estimation. A regression model based on proposed model was introduced. Finally, three applications to real data were provided to illustrate the potentiality of the family of distributions.

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 On The Transmuted Powered Moment Exponential Distribution

2021 ◽  
pp. 32-46
Author(s):  
Zafar Iqbal ◽  
Muhammad Rashad ◽  
Abdur Razaq ◽  
Muhammad Salman ◽  
Afsheen Javed
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Survival Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Rate Function ◽  
Data Sets ◽  
Inequality Measures ◽  
New Class

We introduce a new class of lifetime models called the transmuted powered moment exponential distribution. More specifically, the transmuted powered moment exponential distribution covers several new distributions. Survival analysis including survival function, hazard rate function and other related measures are computed. Analytical expressions for various mathematical properties of TPMED including rth moment, quantile function, inequality measures, and parameters are estimated by using maximum likelihood estimation and order statistics are also derived. A simulation study of the proposed distribution is performed. It is discovered that the Maximum Likelihood Estimators are consistent since the bias and Mean Square Error approach to zero when the sample size increases. The usefulness of the model associated with this distribution is illustrated by two real data sets and the new model provides a better fit than the models provided in literature.

Inverse Akash distribution and its applications

2021 ◽  
Vol 20 (2) ◽  
pp. 61-72
Author(s):  
E.W. Okereke ◽  
S.N. Gideon ◽  
J. Ohakwe
Keyword(s):  
Survival Function ◽  
Likelihood Estimation ◽  
Stochastic Ordering ◽  
Real Data ◽  
Rate Function ◽  
Entropy Measure ◽  
Parameter Distribution ◽  
Data Sets ◽  
Inverse Exponential Distribution ◽  
Inverse Lindley Distribution

A new one-parameter distribution named inverse Akash distribution, for modelling lifetime data, has been  introduced. Important statistical properties of the proposed distribution such as the density function, hazard rate function, survival function, stochastic ordering,  entropy   measure, stress-strength reliability and the maximum  likelihood estimation of the parameter of the distribution have been discussed. Two real data sets were employed in illustrating the usefulness of the new distribution. Comparatively, the inverse Akash distribution provided better fits to the data than each of the inverse exponential distribution and inverse Lindley distribution.

scholarly journals A New Flexible Generalized Lindley Model: Properties, Estimation and Applications

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1678
Author(s):  
Abdulrahman Abouammoh ◽  
Mohamed Kayid
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Moment Generating Function ◽  
Rate Function ◽  
Failure Rate Function ◽  
Right Censored Data ◽  
Special Cases ◽  
The Moment ◽  
The Right

A new method for generalizing the Lindley distribution, by increasing the number of mixed models is presented formally. This generalized model, which is called the generalized Lindley of integer order, encompasses the exponential and the usual Lindley distributions as special cases when the order of the model is fixed to be one and two, respectively. The moments, the variance, the moment generating function, and the failure rate function of the initiated model are extracted. Estimation of the underlying parameters by the moment and the maximum likelihood methods are acquired. The maximum likelihood estimation for the right censored data has also been discussed. In a simulation running for various orders and censoring rates, efficiency of the maximum likelihood estimator has been explored. The introduced model has ultimately been fitted to two real data sets to emphasize its application.

scholarly journals The Topp-Leone odd log-logistic Gumbel Distribution: Properties and Applications

2020 ◽  
Vol 9 (2) ◽  
pp. 288-310
Author(s):  
Fazlollah Lak ◽  
Morad Alizadeh ◽  
Hamid Karamikabir
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Hazard Rate ◽  
Gumbel Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Rate Function ◽  
Model Parameters ◽  
Data Sets ◽  
Hazard Rate Function

In this article, the Topp-Leone odd log-logistic Gumbel (TLOLL-Gumbel) family of distribution have beenstudied. This family, contains the very flexible skewed density function. We study many aspects of the new model like hazard rate function, asymptotics, useful expansions, moments, generating Function, R´enyi entropy and order statistics. We discuss maximum likelihood estimation of the model parameters. Further, we study flexibility of the proposed family are illustrated of two real data sets.

scholarly journals A New Lindley-Burr XII Distribution: Model, Properties and Applications

2021 ◽  
Vol 10 (4) ◽  
pp. 33
Author(s):  
Boikanyo Makubate ◽  
Broderick Oluyede ◽  
Morongwa Gabanakgosi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Real Data ◽  
Distribution Model ◽  
Model Parameters ◽  
Data Sets ◽  
Mean Square ◽  
Conditional Moments ◽  
New Distribution

A new distribution called the Lindley-Burr XII (LBXII) distribution is proposed and studied. Some structural properties of the new distribution including moments, conditional moments, distribution of the order statistics and R´enyi entropy are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A simulation study to examine the bias and mean square error of the maximum likelihood estimators is presented and applications to real data sets in order to illustrate the usefulness of the new distribution are given.

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