The Topp Leone Kumaraswamy-G Family of Distributions with Applications to Cancer Disease Data

2020 ◽  
Author(s):  
Ibrahim Sule ◽  
Sani Ibrahim Doguwa ◽  
Audu Isah ◽  
Haruna Muhammad Jibril
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Logistic Distribution ◽  
Data Sets ◽  
Medical Sciences ◽  
Cancer Disease ◽  
Underlying Distribution ◽  
New Family ◽  
The Family ◽  
Family Of Distributions

Background: In the last few years, statisticians have introduced new generated families of univariate distributions. These new generators are obtained by adding one or more extra shape parameters to the underlying distribution to get more flexibility in fitting data in different areas such as medical sciences, economics, finance and environmental sciences. The addition of parameter(s) has been proven useful in exploring tail properties and also for improving the goodness-of-fit of the family of distributions under study. Methods: A new three-parameter family of distributions was introduced by using the idea of T-X methodology. Some statistical properties of the new family were derived and studied. Results: A new Topp Leone Kumaraswamy-G family of distributions was introduced. Two special sub-models, that is, the Topp Leone Kumaraswamy exponential distribution and Topp Leone Kumaraswamy log-logistic distribution were investigated. Two real data sets were used to assess the flexibility of the sub-models. Conclusion: The results suggest that the two sub-models performed better than their competitors.

scholarly journals The Generalized Additive Weibull-G Family of Distributions

2017 ◽  
Vol 6 (5) ◽  
pp. 65 ◽  
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.

Truncated log-logistic Family of Distributions

2020 ◽  
Author(s):  
Mohadese Akbarinasab ◽  
Ali Reza Arabpour ◽  
Abbas Mahdavi
Keyword(s):  
Goodness Of Fit ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Real Dataset ◽  
New Family ◽  
The Family ◽  
The World ◽  
Family Of Distributions ◽  
Better Than

Background & Aim: There are various data associated with any events in the world which need to be analyzed. In response to this, many researchers attempt to find appropriate methods that could better fit these data using new models. One of these methods is to introduce new distributions which could better describe available data. During last few years, new distributions have been extended based on existing well-known distributions. Usually, new distributions have more parameters than existing ones. This addition of parameter(s) has been proved useful in exploring tail properties and also for improving the goodness-of-fit of the family under study. Methods & Materials: A new family of distributions is introduced by using truncated log-logistic distribution. Some statistical and reliability properties of the new family are derived. Results: Four special lifetime models of the new family are investigated. We estimate the parameters by maximum likelihood method. The obtained results are validated using a real dataset and it is shown that the new distributions provide a better fit than some other known distributions. Conclusion: We have provided four new distributions. The flexibility of the proposed distributions and increased range of skewness was able to fit and capture features in one real dataset much better than some competitor distributions

scholarly journals On the Topp Leone Exponentiated-G Family of Distributions: Properties and Applications

2020 ◽  
pp. 1-15 ◽  
Author(s):  
Sule Ibrahim ◽  
Sani Ibrahim Doguwa ◽  
Isah Audu ◽  
Jibril Haruna Muhammad
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Quantile Function ◽  
Data Sets ◽  
Shape Parameters ◽  
New Family ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
The Family ◽  
Family Of Distributions

We proposed a new family of distributions called the Topp Leone exponentiated-G family of distributions with two extra positive shape parameters, which generalizes and also extends the Topp Leone-G family of distributions. We derived some mathematical properties of the proposed family including explicit expressions for the quantile function, ordinary and incomplete moments, generating function and reliability. Some sub-models in the new family were discussed. The method of maximum likelihood was used to estimate the parameters of the sub-model. Further, the potentiality of the family was illustrated by fitting two real data sets to the mentioned sub-models.

scholarly journals The Alpha-Beta Skew Logistic Distribution: Properties and Applications

2020 ◽  
Vol 8 (1) ◽  
pp. 304-317 ◽  
Author(s):  
Hamid Esmaeili ◽  
Fazlollah Lak ◽  
Morad Alizadeh ◽  
Mohammad esmail Dehghan monfared
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Real Data ◽  
Logistic Distribution ◽  
Data Sets ◽  
New Family ◽  
Alpha Beta ◽  
Family Of Distributions ◽  
Skewness And Kurtosis

A new family of skew distributions is introduced by extending the alpha skew logistic distribution proposed by Hazarika-Chakraborty [9]. This family of distributions is called the alpha-beta skew logistic (ABSLG) distribution.Density function, moments, skewness and kurtosis coefficients are derived. The parameters of the new family are estimated by maximum likelihood and moments methods. The performance of the obtained estimators examined via a Monte carlo simulation. Flexibility, usefulness and suitability of ABSLG is illustrated by analyzing two real data sets.

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.

A New-Flexible Generated Family of Distributions Based on Half-Logistic Distribution

2020 ◽  
Vol 17 (11) ◽  
pp. 4813-4818
Author(s):  
Sanaa Al-Marzouki ◽  
Sharifah Alrajhi
Keyword(s):  
Logistic Model ◽  
Real Data ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Data Set ◽  
New Family ◽  
Probability Weighted Moment ◽  
The Subject ◽  
Generated Family ◽  
Family Of Distributions

We proposed a new family of distributions from a half logistic model called the generalized odd half logistic family. We expressed its density function as a linear combination of exponentiated densities. We calculate some statistical properties as the moments, probability weighted moment, quantile and order statistics. Two new special models are mentioned. We study the estimation of the parameters for the odd generalized half logistic exponential and the odd generalized half logistic Rayleigh models by using maximum likelihood method. One real data set is assesed to illustrate the usefulness of the subject family.

scholarly journals Extended Odd Fréchet-G Family of Distributions

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
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.

scholarly journals Odd Lomax-Kumaraswamy Distribution: Its Properties and Applications

2020 ◽  
pp. 45-60
Author(s):  
Bassa Shiwaye Yakura ◽  
Ahmed Askira Sule ◽  
Mustapha Mohammed Dewu ◽  
Kabiru Ahmed Manju ◽  
Fadimatu Bawuro Mohammed
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Distribution Functions ◽  
Model Parameters ◽  
Data Sets ◽  
Kumaraswamy Distribution ◽  
Method Of Maximum Likelihood ◽  
Family Of Distributions

This article uses the odd Lomax-G family of distributions to study a new extension of the Kumaraswamy distribution called “odd Lomax-Kumaraswamy distribution”. In this article, the density and distribution functions of the odd Lomax-Kumaraswamy distribution are defined and studied with many other properties of the distribution such as the ordinary moments, moment generating function, characteristic function, quantile function, reliability functions, order statistics and other useful measures. The model parameters are estimated by the method of maximum likelihood. The goodness-of-fit of the proposed distribution is demonstrated using two real data sets.

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 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.  

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