A New Family of Generalized Distributions Based on Alpha Power Transformation with Application to Cancer Data

2018 ◽  
Vol 5 (3) ◽  
pp. 421-436 ◽  
Author(s):  
M. Nassar ◽  
A. Alzaatreh ◽  
O. Abo-Kasem ◽  
M. Mead ◽  
M. Mansoor
Keyword(s):  
Power Transformation ◽  
Alpha Power ◽  
Cancer Data ◽  
New Family ◽  
Generalized Distributions

scholarly journals The Censored Beta-Skew Alpha-Power Distribution

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1114
Author(s):  
Guillermo Martínez-Flórez ◽  
Roger Tovar-Falón ◽  
María Martínez-Guerra
Keyword(s):  
Power Distribution ◽  
Information Matrix ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Alpha Power ◽  
Score Functions ◽  
New Family ◽  
Two Parameters ◽  
Family Of Distributions

This paper introduces a new family of distributions for modelling censored multimodal data. The model extends the widely known tobit model by introducing two parameters that control the shape and the asymmetry of the distribution. Basic properties of this new family of distributions are studied in detail and a model for censored positive data is also studied. The problem of estimating parameters is addressed by considering the maximum likelihood method. The score functions and the elements of the observed information matrix are given. Finally, three applications to real data sets are reported to illustrate the developed methodology.

scholarly journals The Alpha Power Transformation Family: Properties and Applications

2019 ◽  
pp. 525-545 ◽  
Author(s):  
Mohamed E. Mead ◽  
Gauss M. Cordeiro ◽  
Ahmed Z. Afify ◽  
Hazem Al Mofleh
Keyword(s):  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Power Transformation ◽  
Data Sets ◽  
Alpha Power ◽  
Weibull Distributions ◽  
Exponentiated Weibull ◽  
Rate Functions ◽  
Modified Weibull

Mahdavi A. and Kundu D. (2017) introduced a family for generating univariate distributions called the alpha power transformation. They studied as a special case the properties of the alpha power transformed exponential distribution. We provide some mathematical properties of this distribution and define a four-parameter lifetime model called the alpha power exponentiated Weibull distribution. It generalizes some well-known lifetime models such as the exponentiated exponential, exponentiated Rayleigh, exponentiated Weibull and Weibull distributions. The importance of the new distribution comes from its ability to model monotone and non-monotone failure rate functions, which are quite common in reliability studies. We derive some basic properties of the proposed distribution including quantile and generating functions, moments and order statistics. The maximum likelihood method is used to estimate the model parameters. Simulation results investigate the performance of the estimates. We illustrate the importance of the proposed distribution over the McDonald Weibull, beta Weibull, modified Weibull, transmuted Weibull and exponentiated Weibull distributions by means of two real data sets.

A new family of generalized distributions

2011 ◽  
Vol 81 (7) ◽  
pp. 883-898 ◽  
Author(s):  
Gauss M. Cordeiro ◽  
Mário de Castro
Keyword(s):  
New Family ◽  
Generalized Distributions

scholarly journals The Beta Weibull-G Family of Distributions: Model, Properties and Application

2018 ◽  
Vol 7 (2) ◽  
pp. 12 ◽  
Author(s):  
Boikanyo Makubate ◽  
Broderick O. Oluyede ◽  
Gofaone Motobetso ◽  
Shujiao Huang ◽  
Adeniyi F. Fagbamigbe
Keyword(s):  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Exponential Distributions ◽  
Data Set ◽  
New Class ◽  
New Family ◽  
Generalized Distributions ◽  
Special Cases

A new family of generalized distributions called the beta Weibull-G (BWG) distribution is proposed and developed. This new class of distributions has several new and well known distributions including exponentiated-G, Weibull-G, Rayleigh-G, exponential-G, beta exponential-G, beta Rayleigh-G, beta Rayleigh exponential, beta-exponential-exponential, Weibull-log-logistic distributions, as well as several other distributions such as beta Weibull-Uniform, beta Rayleigh-Uniform, beta exponential-Uniform, beta Weibull-log logistic and beta Weibull-exponential distributions as special cases. Series expansion of the density function, hazard function, moments, mean deviations, Lorenz and Bonferroni curves, R\'enyi entropy, distribution of order statistics and maximum likelihood estimates of the model parameters are given. Application of the model to real data set is presented to illustrate the importance and usefulness of the special case beta Weibull-log-logistic distribution.

scholarly journals Gull Alpha Power of the Chen Type

2020 ◽  
pp. 16-17
Author(s):  
Ampadu Clement Boateng
Keyword(s):  
Power Distribution ◽  
Real Life ◽  
Alpha Power ◽  
Life Data ◽  
New Family ◽  
Real Life Data

In they introduced the Chen distribution, and in they extended the distribution to include its “normalized version”. In this paper, we introduce a variant of the Gull Alpha Power distribution by modifying Chen-G of and show the new family is good in fitting real life data.

scholarly journals A New Modified Kies Family: Properties, Estimation Under Complete and Type-II Censored Samples, and Engineering Applications

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1345 ◽  
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Mohammed K. Shakhatreh ◽  
Mazen Nassar ◽  
Ahmed Z. Afify
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Real Data ◽  
Mean Residual Life ◽  
Type Ii ◽  
Censored Samples ◽  
New Family ◽  
Generalized Distributions ◽  
Two Parameters ◽  
New Distribution

In this paper, we introduce a new family of continuous distributions that is called the modified Kies family of distributions. The main mathematical properties of the new family are derived. A special case of the new family has been considered in more detail; namely, the two parameters modified Kies exponential distribution with bathtub shape, decreasing and increasing failure rate function. The importance of the new distribution comes from its ability in modeling positively and negatively skewed real data over some generalized distributions with more than two parameters. The shape behavior of the hazard rate and the mean residual life functions of the modified Kies exponential distribution are discussed. We use the method of maximum likelihood to estimate the distribution parameters based on complete and type-II censored samples. The approximate confidence intervals are also obtained under the two schemes. A simulation study is conducted and two real data sets from the engineering field are analyzed to show the flexibility of the new distribution in modeling real life data.

scholarly journals Likelihood-Based Inference for the Asymmetric Beta-Skew Alpha-Power Distribution

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 613
Author(s):  
Guillermo Martínez-Flórez ◽  
Roger Tovar-Falón ◽  
Marvin Jimémez-Narváez
Keyword(s):  
Power Distribution ◽  
Information Matrix ◽  
Likelihood Method ◽  
Data Sets ◽  
Alpha Power ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
New Family ◽  
Asymmetric Distributions ◽  
Two Parameters

This paper introduces a new family of asymmetric distributions that allows to fit unimodal as well as bimodal and trimodal data sets. The model extends the normal model by introducing two parameters that control the shape and the asymmetry of the distribution. Basic properties of this new distribution are studied in detail. The problem of estimating parameters is addressed by considering the maximum likelihood method and Fisher information matrix is derived. A small Monte Carlo simulation study is conducted to examine the performance of the obtained estimators. Finally, two data set are considered to illustrate the developed methodology.

scholarly journals Alpha Power Transformed Extended Bur II Distribution: Properties and Applications

2020 ◽  
pp. 50-63
Author(s):  
A. A. Ogunde ◽  
B. Ajayi ◽  
D. O. Omosigho
Keyword(s):  
Estimation Method ◽  
Likelihood Estimation ◽  
Moment Generating Function ◽  
Power Transformation ◽  
Data Sets ◽  
Alpha Power ◽  
Real World Data ◽  
Mathematical Properties ◽  
Maximum Likelihood Estimation Method ◽  
New Distribution

This paper presents a new generalization of the extended Bur II distribution. We redefined the Bur II distribution using the Alpha Power Transformation (APT) to obtain a new distribution called the Alpha Power Transformed Extended Bur II distribution. We derived several mathematical properties for the new model which includes moments, moment generating function, order statistics, entropy etc. and used a maximum likelihood estimation method to obtain the parameters of the distribution. Two real-world data sets were used for applications in order to illustrate the usefulness of the new distribution.

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