scholarly journals A New Lifetime Exponential-X Family of Distributions with Applications to Reliability Data

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Xiaoyan Huo ◽  
Saima K. Khosa ◽  
Zubair Ahmad ◽  
Zahra Almaspoor ◽  
Muhammad Ilyas ◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Model Parameters ◽  
Reliability Engineering ◽  
Reliability Data ◽  
Monte Carlo Simulation Study ◽  
Hazard Functions ◽  
Practical Applications ◽  
New Family ◽  
Nonnested Models ◽  
Family Of Distributions

Modeling reliability data with nonmonotone hazards is a prominent research topic that is quite rich and still growing rapidly. Many studies have suggested introducing new families of distributions to modify the Weibull distribution to model the nonmonotone hazards. In the present study, we propose a new family of distributions called a new lifetime exponential-X family. A special submodel of the proposed family called a new lifetime exponential-Weibull distribution suitable for modeling reliability data with bathtub-shaped hazard rates is discussed. The maximum-likelihood estimators of the model parameters are obtained. A brief Monte Carlo simulation study is conducted to evaluate the performance of these estimators. For illustrative purposes, two real applications from reliability engineering with bathtub-shaped hazard functions are analyzed. The practical applications show that the proposed model provides better fits than the other nonnested models.

scholarly journals A New Flexible Bathtub-Shaped Modification of the Weibull Model: Properties and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Qinghu Liao ◽  
Zubair Ahmad ◽  
Eisa Mahmoudi ◽  
G. G. Hamedani
Keyword(s):  
Weibull Distribution ◽  
Hazard Rate ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Weibull Model ◽  
Rate Function ◽  
Model Parameters ◽  
Hazard Functions ◽  
Practical Applications ◽  
Nonnested Models

Many studies have suggested the modifications and generalizations of the Weibull distribution to model the nonmonotone hazards. In this paper, we combine the logarithms of two cumulative hazard rate functions and propose a new modified form of the Weibull distribution. The newly proposed distribution may be called a new flexible extended Weibull distribution. Corresponding hazard rate function of the proposed distribution shows flexible (monotone and nonmonotone) shapes. Three different characterizations along with some mathematical properties are provided. We also consider the maximum likelihood estimation procedure to estimate the model parameters. For the illustrative purposes, two real applications from reliability engineering with bathtub-shaped hazard functions are analyzed. The practical applications show that the proposed model provides better fits than the other nonnested models.

scholarly journals The Generalized Ampadu-G Family of Distributions: Properties, Applications and Characterizations

2020 ◽  
pp. 139-167
Author(s):  
Clement Boateng Ampadu ◽  
Abdulzeid Yen Anafo
Keyword(s):  
Weibull Distribution ◽  
Density Function ◽  
Survival Function ◽  
Real Life ◽  
Life Time ◽  
Quantile Function ◽  
Cumulative Distribution ◽  
Model Parameters ◽  
New Family ◽  
Family Of Distributions

This paper introduces a new class of distributions called the generalized Ampadu-G (GA-G for short) family of distributions, and with a certain restriction on the parameter space, the family is shown to be a life-time distribution. The shape of the density function and hazard rate function of the GA-G family is described analytically. When G follows the Weibull distribution, the generalized Ampadu-Weibull (GA-W for short) is presented along with its hazard and survival function. Several sub-models of the GA-W family are presented. The transformation technique is applied to this new family of distributions, and we obtain the quantile function of the new family. Power series representations for the cumulative distribution function (CDF) and probability density function (PDF) are also obtained. The rth non-central moments, moment generating function, and Renyi entropy associated with the new family of distributions are derived. Characterization theorems based on two truncated moments and conditional expectation are also presented. A simulation study is also conducted, and we find that using the method of maximum likelihood to estimate model parameters is adequate. The GA-W family of distributions is shown to be practically significant in modeling real life data, and is shown to be superior to some non-trivial generalizations of the Weibull distribution. A further development concludes the paper.

scholarly journals A Flexible Reduced Logarithmic-X Family of Distributions with Biomedical Analysis

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Yinglin Liu ◽  
Muhammad Ilyas ◽  
Saima K. Khosa ◽  
Eisa Muhmoudi ◽  
Zubair Ahmad ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Medical Data ◽  
Model Parameters ◽  
Data Sets ◽  
Biomedical Sciences ◽  
Biomedical Analysis ◽  
Monte Carlo Simulation Study ◽  
New Family ◽  
The Right ◽  
Family Of Distributions

Statistical distributions play a prominent role in applied sciences, particularly in biomedical sciences. The medical data sets are generally skewed to the right, and skewed distributions can be used quite effectively to model such data sets. In the present study, therefore, we propose a new family of distributions to model right skewed medical data sets. The proposed family may be named as a flexible reduced logarithmic-X family. The proposed family can be obtained via reparameterizing the exponentiated Kumaraswamy G-logarithmic family and the alpha logarithmic family of distributions. A special submodel of the proposed family called, a flexible reduced logarithmic-Weibull distribution, is discussed in detail. Some mathematical properties of the proposed family and certain related characterization results are presented. The maximum likelihood estimators of the model parameters are obtained. A brief Monte Carlo simulation study is done to evaluate the performance of these estimators. Finally, for the illustrative purposes, three applications from biomedical sciences are analyzed and the goodness of fit of the proposed distribution is compared to some well-known competitors.

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

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1837
Author(s):  
Emrah Altun ◽  
Mustafa Ç. Korkmaz ◽  
Mahmoud El-Morshedy ◽  
Mohamed S. Eliwa
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Additive Model ◽  
Maximum Likelihood Estimators ◽  
Model Parameters ◽  
Model Structure ◽  
Simulation Studies ◽  
New Family ◽  
Family Based ◽  
Family Of Distributions

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.

scholarly journals A Study on A New Type 1 Half-Logistic Family of Distributions and Its Applications

2020 ◽  
Vol 8 (4) ◽  
pp. 934-949
Author(s):  
Morad Alizadeh ◽  
Alireza Nematollahi ◽  
Emrah Altun ◽  
Mahdi Rasekhi
Keyword(s):  
Residual Life ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Mean Deviation ◽  
Model Parameters ◽  
Type I ◽  
Monte Carlo Simulation Study ◽  
New Type ◽  
Application Fields ◽  
Family Of Distributions

In this paper, we propose a new class of continuous distributions with two extra shape parameters called the a new type I half logistic-G family of distributions. Some of important properties including ordinary moments, quantiles, moment generating function, mean deviation, moment of residual life, moment of reversed residual life, order statistics and extreme value are obtained. To estimate the model parameters, the maximum likelihood method is also applied by means of Monte Carlo simulation study. A new location-scale regression model based on the new type I half logistic-Weibull distribution is then introduced. Applications of the proposed family is demonstrated in many fields such as survival analysis and univariate data fitting. Empirical results show that the proposed models provide better fits than other well-known classes of distributions in many application fields.

scholarly journals The Marshall-Olkin Half Logistic-G Family of Distributions With Applications

2021 ◽  
Vol 10 (2) ◽  
pp. 119
Author(s):  
Boikanyo Makubate ◽  
Fastel Chipepa ◽  
Broderick Oluyede ◽  
Peter O. Peter
Keyword(s):  
Survival Analysis ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Simulation Experiments ◽  
New Family ◽  
Modeling Data ◽  
Engineering Hydrology ◽  
Family Of Distributions

Attempts have been made to define new classes of distributions that provide more flexibility for modeling data that is skewed in nature. In this work, we propose a new family of distributions namely the Marshall-Olkin Half Logistic-G (MO-HL-G) based on the generator pioneered by [Marshall and Olkin , 1997]. This new family of distributions allows for a flexible fit to real data from several fields, such as engineering, hydrology, and survival analysis. The structural properties of these distributions are studied and its model parameters are obtained through the maximum likelihood method. We finally demonstrate the effectiveness of these models via simulation experiments.

scholarly journals Truncated Inverted Kumaraswamy Generated Family of Distributions with Applications

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1089 ◽  
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Rate Function ◽  
Parametric Models ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Full Generality ◽  
Kumaraswamy Distribution ◽  
New Family ◽  
Generated Family ◽  
Family Of Distributions

In this article, we introduce a new general family of distributions derived to the truncated inverted Kumaraswamy distribution (on the unit interval), called the truncated inverted Kumaraswamy generated family. Among its qualities, it is characterized with tractable functions, has the ability to enhance the flexibility of a given distribution, and demonstrates nice statistical properties, including competitive fits for various kinds of data. A particular focus is given on a special member of the family defined with the exponential distribution as baseline, offering a new three-parameter lifetime distribution. This new distribution has the advantage of having a hazard rate function allowing monotonically increasing, decreasing, and upside-down bathtub shapes. In full generality, important properties of the new family are determined, with an emphasis on the entropy (Rényi and Shannon entropy). The estimation of the model parameters is established by the maximum likelihood method. A numerical simulation study illustrates the nice performance of the obtained estimates. Two practical data sets are then analyzed. We thus prove the potential of the new model in terms of fitting, with favorable results in comparison to other modern parametric models of the literature.

scholarly journals A New Extended-X Family of Distributions: Properties and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Mi Zichuan ◽  
Saddam Hussain ◽  
Anum Iftikhar ◽  
Muhammad Ilyas ◽  
Zubair Ahmad ◽  
...  
Keyword(s):  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Statistical Distributions ◽  
Reliability Engineering ◽  
Monte Carlo Simulation Study ◽  
Diverse Range ◽  
Heavy Tailed ◽  
Log Normal ◽  
Extended Weibull Distribution

During the past couple of years, statistical distributions have been widely used in applied areas such as reliability engineering, medical, and financial sciences. In this context, we come across a diverse range of statistical distributions for modeling heavy tailed data sets. Well-known distributions are log-normal, log-t, various versions of Pareto, log-logistic, Weibull, gamma, exponential, Rayleigh and its variants, and generalized beta of the second kind distributions, among others. In this paper, we try to supplement the distribution theory literature by incorporating a new model, called a new extended Weibull distribution. The proposed distribution is very flexible and exhibits desirable properties. Maximum likelihood estimators of the model parameters are obtained, and a Monte Carlo simulation study is conducted to assess the behavior of these estimators. Finally, we provide a comparative study of the newly proposed and some other existing methods via analyzing three real data sets from different disciplines such as reliability engineering, medical, and financial sciences. It has been observed that the proposed method outclasses well-known distributions on the basis of model selection criteria.

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 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.

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