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

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.

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Extended Odd Fréchet-G Family of Distributions

Journal of Probability and Statistics ◽

10.1155/2018/2931326 ◽

2018 ◽

Vol 2018 ◽

pp. 1-12 ◽

Cited By ~ 6

Author(s):

Suleman Nasiru

Keyword(s):

Maximum Likelihood Method ◽

Real Data ◽

Likelihood Method ◽

Data Sets ◽

Data Set ◽

New Class ◽

New Family ◽

Rate Functions ◽

The Given ◽

Family Of Distributions

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.

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The Generalized Additive Weibull-G Family of Distributions

International Journal of Statistics and Probability ◽

10.5539/ijsp.v6n5p65 ◽

2017 ◽

Vol 6 (5) ◽

pp. 65 ◽

Cited By ~ 6

Author(s):

Amal S. Hassan ◽

Saeed E. Hemeda ◽

Sudhansu S. Maiti ◽

Sukanta Pramanik

Keyword(s):

Maximum Likelihood Method ◽

Real Data ◽

Random Variable ◽

Likelihood Method ◽

Parameter Estimates ◽

Data Sets ◽

New Family ◽

The Family ◽

Generated Family ◽

Family Of Distributions

In this paper, we present a new family, depending on additive Weibull random variable as a generator, called the generalized additive Weibull generated-family (GAW-G) of distributions with two extra parameters. The proposed family involves several of the most famous classical distributions as well as the new generalized Weibull-G family which already accomplished by Cordeiro et al. (2015). Four special models are displayed. The expressions for the incomplete and ordinary moments, quantile, order statistics, mean deviations, Lorenz and Benferroni curves are derived. Maximum likelihood method of estimation is employed to obtain the parameter estimates of the family. The simulation study of the new models is conducted. The efficiency and importance of the new generated family is examined through real data sets.

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Modified generalized marshall-olkin family of distributions

International Journal of Advanced Statistics and Probability ◽

10.14419/ijasp.v7i1.28916 ◽

2019 ◽

Vol 7 (1) ◽

pp. 18

Author(s):

Muhammad Aslam ◽

Zawar Hussain ◽

Zahid Asghar

Keyword(s):

Maximum Likelihood ◽

Goodness Of Fit ◽

Maximum Likelihood Method ◽

Likelihood Estimation ◽

Likelihood Method ◽

Model Parameters ◽

Data Sets ◽

Goodness Of Fit Tests ◽

New Family ◽

Family Of Distributions

In this article, we propose a new family of distributions using the T-X family named as modified generalized Marshall-Olkin family of distributions. Comprehensive mathematical and statistical properties of this family of distributions are provided. The model parameters are estimated by maximum likelihood method. The maximum likelihood estimation under Type-II censoring is also discussed. Two lifetime data sets are used to show the suitability and applicability of the new family of distributions. For comparison purposes, different goodness of fit tests are used.

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A New One-parameter G Family of Compound Distributions: Copulas, Statistical Properties and Applications

Statistics Optimization & Information Computing ◽

10.19139/soic-2310-5070-1239 ◽

2021 ◽

Vol 9 (4) ◽

pp. 942-962

Author(s):

Mohamed Abo Raya

Keyword(s):

Maximum Likelihood ◽

Hazard Function ◽

Maximum Likelihood Method ◽

Real Data ◽

Heavy Tail ◽

Statistical Properties ◽

Likelihood Method ◽

Model Parameters ◽

Data Sets ◽

New Family

This work introduces a new one-parameter compound G family. Relevant statistical properties are derived. The new density can be “asymmetric right skewed with one peak and a heavy tail”, “symmetric” and “left skewedwith one peak”. The new hazard function can be “upside-down”, “upside-down-constant”, “increasing”, “decreasing” and “decreasing-constant”. Many bivariate types have been also derived via different common copulas. The estimation of the model parameters is performed by maximum likelihood method. The usefulness and flexibility of the new family is illustrated by means of two real data sets.

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The Odd Power Lindley Generator of Probability Distributions: Properties, Characterizations and Regression Modeling

International Journal of Statistics and Probability ◽

10.5539/ijsp.v8n2p70 ◽

2019 ◽

Vol 8 (2) ◽

pp. 70 ◽

Cited By ~ 17

Author(s):

Mustafa C. Korkmaz ◽

Emrah Altun ◽

Haitham M. Yousof ◽

G.G. Hamedani

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Method ◽

Probability Distributions ◽

Real Data ◽

Likelihood Method ◽

Model Parameters ◽

Data Sets ◽

Simulation Studies ◽

Proposed Model ◽

Family Of Distributions

In this study, a new flexible family of distributions is proposed with its statistical properties as well as some useful characterizations. The maximum likelihood method is used to estimate the unknown model parameters by means of two simulation studies. A new regression model is proposed based on a special member of the proposed family called, the log odd power Lindley Weibull distribution. Residual analysis is conducted to evaluate the model assumptions. Four applications to real data sets are given to demonstrate the usefulness of the proposed model.

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Generalized Flexible Weibull Extension Distribution

Circulation in Computer Science ◽

10.22632/ccs-2017-252-11 ◽

2017 ◽

Vol 2 (4) ◽

pp. 68-75

Author(s):

Zubair Ahmad ◽

Brikhna Iqbal

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Method ◽

Real Data ◽

Likelihood Method ◽

Model Parameters ◽

Data Sets ◽

Suggested Model ◽

Proposed Model ◽

Parameter Values ◽

Family Of Distributions

In this article, a four parameter generalization of the flexible Weibull extension distribution so-called generalized flexible Weibull extension distribution is studied. The proposed model belongs to T-X family of distributions proposed by Alzaatreh et al. [5]. The suggested model is much flexible and accommodates increasing, unimodal and modified unimodal failure rates. A comprehensive expression of the numerical properties and the estimates of the model parameters are obtained using maximum likelihood method. By appropriate choice of parameter values the new model reduces to four sub models. The proposed model is illustrated by means of three real data sets.

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Truncated Cauchy Power Odd Fréchet-G Family of Distributions: Theory and Applications

Complexity ◽

10.1155/2021/4256945 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

M. Shrahili ◽

I. Elbatal

Keyword(s):

Maximum Likelihood Method ◽

Exponential Model ◽

Likelihood Method ◽

Mean Deviation ◽

Model Parameters ◽

Lorenz Curves ◽

New Family ◽

The Family ◽

Real World Datasets ◽

Family Of Distributions

The truncated Cauchy power odd Fréchet-G family of distributions is presented in this article. This family’s unique models are launched. Statistical properties of the new family are proposed, such as density function expansion, moments, incomplete moments, mean deviation, Bonferroni and Lorenz curves, and entropy. We investigate the maximum likelihood method for predicting model parameters of the new family. Two real-world datasets are used to show the importance and flexibility of the new family by using the truncated Cauchy power odd Fréchet exponential model as example of the family and compare it with some known models, and this model proves the importance and the flexibility for the new family.

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The four-parameter Fréchet distribution: Properties and applications

Pakistan Journal of Statistics and Operation Research ◽

10.18187/pjsor.v16i2.3097 ◽

2020 ◽

pp. 249-264

Author(s):

Mohamed Hamed ◽

Fahad Aldossary ◽

Ahmed Z. Afify

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Method ◽

Real Data ◽

Maximum Likelihood Estimates ◽

Likelihood Method ◽

Model Parameters ◽

Fréchet Distribution ◽

Mathematical Properties ◽

Modeling Data ◽

Frechet Distribution

In this article, we propose a new four-parameter Fréchet distribution called the odd Lomax Fréchet distribution. The new model can be expressed as a linear mixture of Fréchet densities. We provide some of its mathematical properties. The estimation of the model parameters is performed by the maximum likelihood method. We illustrate the good performance of the maximum likelihood estimates via a detailed numerical simulation study. The importance and usefulness of the proposed distribution for modeling data are illustrated using two real data applications.

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The Censored Beta-Skew Alpha-Power Distribution

Symmetry ◽

10.3390/sym13071114 ◽

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.

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