scholarly journals The Topp Leone Generalized Inverted Kumaraswamy Distribution: Properties and Applications

2019 ◽  
pp. 1-15 ◽  
Author(s):  
Hesham Reyad ◽  
Farrukh Jamal ◽  
Soha Othman ◽  
Nagla Yahia
Keyword(s):  
Stochastic Ordering ◽  
Quantile Function ◽  
Continuous Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Kumaraswamy Distribution ◽  
Mathematical Properties ◽  
Probability Weighted Moments ◽  
Method Of Maximum Likelihood ◽  
New Distribution

We propose a new four parameters continuous model called the Topp Leone generalized inverted Kumaraswamy distribution which extends the generalized inverted Kumaraswamy distribution. Basic mathematical properties of the new distribution are invstigated such as; quantile function, raw and incomplete moments, generating functions, probability weighted moments, order statistics, Rényi entropy, stochastic ordering and stress strength model. The method of maximum likelihood is used to estimate the model parameters of the new distribution. A Monte Carlo simulation is conducted to examine the behavior of the parameter estimates. The applicability of the new model is demonstrated by means of two real applications.

MATHEMATICAL PROPERTIES AND APPLICATIONS OF MINIMUM GUMBEL BURR DISTRIBUTION

2020 ◽  
Vol XVII (2) ◽  
pp. 1-14
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Syed Muhammad Akbar Ali Shah
Keyword(s):  
Stochastic Ordering ◽  
Quantile Function ◽  
Continuous Model ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Parameter Estimates ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Burr Distribution ◽  
New Distribution

This paper presents the details of a proposed continuous model for the minimum Gumbel Burr distribution which is based on four different parameters. The model is obtained by compounding the Gumbel type-II and Burr-XII distributions. Basic mathematical properties of the new distribution were studied including the quantile function, ordinary and incomplete moments, moment generating function, order statistics, Rényi entropy, stress-strength model and stochastic ordering. The parameters of the proposed distribution are estimated using the maximum likelihood method. A Monte Carlo simulation was presented to examine the behaviour of the parameter estimates. The flexibility of the proposed model was assessed by means of three applications.

MATHEMATICAL PROPERTIES AND APPLICATIONS OF MINIMUM GUMBEL BURR DISTRIBUTION

2020 ◽  
Vol XVII (2) ◽  
pp. 1-14
Author(s):  
Farrukh Jamal ◽  
Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Syed Muhammad Akbar Ali Shah
Keyword(s):  
Stochastic Ordering ◽  
Quantile Function ◽  
Continuous Model ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Parameter Estimates ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Burr Distribution ◽  
New Distribution

This paper presents the details of a proposed continuous model for the minimum Gumbel Burr distribution which is based on four different parameters. The model is obtained by compounding the Gumbel type-II and Burr-XII distributions. Basic mathematical properties of the new distribution were studied including the quantile function, ordinary and incomplete moments, moment generating function, order statistics, Rényi entropy, stress-strength model and stochastic ordering. The parameters of the proposed distribution are estimated using the maximum likelihood method. A Monte Carlo simulation was presented to examine the behaviour of the parameter estimates. The flexibility of the proposed model was assessed by means of three applications.

scholarly journals The Nadarajah Haghighi Topp Leone-G Family of Distributions ‎with Mathematical Properties and Applications

2019 ◽  
Vol 15 (4) ◽  
pp. 849
Author(s):  
Hesham Reyad‎ ◽  
Mahmoud Ali Selim ◽  
Soha Othman
Keyword(s):  
Information Matrix ◽  
Quantile Function ◽  
Model Parameters ◽  
Lorenz Curves ◽  
New Class ◽  
New Family ◽  
Mathematical Properties ◽  
Probability Weighted Moments ◽  
Statistics And Probability ◽  
Method Of Maximum Likelihood

Based on the Nadarajah Haghighi distribution and the Topp Leone-G family in view of the T-X family, we introduce a new generator of continuous distributions with three extra parameters called the Nadarajah Haghighi Topp Leone-G family. Three sub-models of the new class are discussed. Main mathematical properties of the new family are investigated such as; quantile function, raw and incomplete moments, Bonferroni and Lorenz curves, moment and probability generating functions, stress-strength model, Shanon and Rényi entropies, order statistics and probability weighted moments. The model parameters of the new family is estimated by using the method of maximum likelihood and the observed information matrix is also obtained. We introduce two real applications to show the importance of the new family.

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 The Gumbel- Pareto Distribution: Theory and Applications

2019 ◽  
Vol 16 (4) ◽  
pp. 0937
Author(s):  
Saad Et al.
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Numerical Illustration ◽  
Data Set ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
First Time ◽  
New Distribution

In this paper, for the first time we introduce a new four-parameter model called the Gumbel- Pareto distribution by using the T-X method. We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters. Numerical illustration and an application to a real data set are given to show the flexibility and potentiality of the new model.

scholarly journals The Kumaraswamy compound Rayleigh distribution : properties and estimation

2017 ◽  
Vol 5 (1) ◽  
pp. 36
Author(s):  
Hesham Reyad ◽  
Soha A. Othman ◽  
Adil M Younis ◽  
Ahmed M. Hashish
Keyword(s):  
Generating Functions ◽  
Quantile Function ◽  
Continuous Model ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Mathematical Properties ◽  
Record Statistics ◽  
Methods Of Moments ◽  
Mean Variance ◽  
Compound Rayleigh Distribution

We introduce a new four parameter continuous model, called the Kumaraswamy compound Rayleigh (KwCR) distribution that extends the compound Rayleigh distribution. We study some mathematical properties of this distribution such as; mean, variance, coefficient of variation, quantile function, median, ordinary and incomplete moments, skewness, kurtosis, moment and probability generating functions, reliability analysis, Lorenz, Bonferroni and Zenga curves, Rényi of entropy, order statistics and record statistics. We consider the methods of moments and maximum likelihood for estimating the model parameters.

scholarly journals Odd Lindley-Kumaraswamy Distribution: Model, Properties and Application

2020 ◽  
pp. 42-58
Author(s):  
Kuje Samson ◽  
Abubakar, Mohammad Auwal ◽  
Asongo, Iorkaa Abraham ◽  
Alhaji, Ismaila Sulaiman
Keyword(s):  
Goodness Of Fit ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Distribution Functions ◽  
Distribution Model ◽  
Model Parameters ◽  
Kumaraswamy Distribution ◽  
Method Of Maximum Likelihood ◽  
Compound Distribution

This article uses the odd Lindley-G family of distributions to propose and study a new compound distribution called “odd Lindley-Kumaraswamy distribution”. In this article, the density and distribution functions of the odd Lindley-Kumaraswamy distribution are defined and studied by deriving and discussing many properties of the distribution such as the ordinary moments, moment generating function, characteristics function, quantile function, reliability functions, order statistics and other useful measures. The unknown model parameters are also estimated by the method of maximum likelihood. The goodness-of-fit of the proposed distribution is demonstrated using two real life datasets. The results show that the proposed distribution outperforms the other fitted compound models selected for this study and hence it is a flexible generalization of the Kumaraswamy distribution.

scholarly journals On Properties and Applications of Lomax-Gompertz Distribution

2019 ◽  
pp. 1-17
Author(s):  
A. Omale ◽  
O. E. Asiribo ◽  
A. Yahaya
Keyword(s):  
Survival Function ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Model Parameters ◽  
Gompertz Distribution ◽  
Probability Of Survival ◽  
Method Of Maximum Likelihood ◽  
Age Dependent ◽  
New Distribution

This article introduces a new distribution called the Lomax-Gompertz distribution developed through a Lomax Generator proposed in an earlier study. Some statistical properties of the proposed distribution comprising moments, moment generating function, characteristics function, quantile function and the distribution of order statistics were derived. The plots of the probability density function revealed that it is positively skewed. The model parameters have been estimated using the method of maximum likelihood. The plot the of survival function indicates that the Lomax-Gompertz distribution could be used to model time or age-dependent data, where probability of survival is believed to be  decreasing  with time or age. The performance of the Lomax-Gompertz distribution has been compared to other generalizations of the Gompertz distribution using three real-life datasets used in earlier researches.

scholarly journals The Zubair-dagum Distribution

2021 ◽  
pp. 25-35
Author(s):  
O. R. Uwaeme ◽  
N. P. Akpan
Keyword(s):  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Parameter Estimates ◽  
Mathematical Properties ◽  
Dagum Distribution ◽  
Maximum Likelihood Estimation Method ◽  
New Distribution

This article examines the flexibility of the Zubair-G family of distribution using the Dagum distribution. The proposed distribution is called the Zubair-Dagum distribution. The various mathematical properties of this distribution such as the Quantile function, Moments, Moment generating function, Reliability analysis, Entropy and Order statistics were obtained. The parameter estimates of the proposed distribution were also derived and estimated using the maximum likelihood estimation method. The new distribution is right skewed and has various bathtub and monotonically decreasing shapes. Our numerical illustrations using two real-life datasets substantiate the applicability, flexibility and superiority of the proposed distribution over competing distributions.

scholarly journals Extended Rayleigh Distribution: Properties and Application to Failure Data

2021 ◽  
pp. 1-8
Author(s):  
Aladesuyi Alademomi ◽  
Philips Samuel Ademola ◽  
Adefolarin Adekunle David
Keyword(s):  
Real Life ◽  
Quantile Function ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Data Set ◽  
New Model ◽  
Failure Data ◽  
Mathematical Properties ◽  
Real Life Data ◽  
Method Of Maximum Likelihood

This paper introduces a new three parameter Rayleigh distribution which generalizes the Rayleigh distribution. The new model is referred to as Extended Rayleigh (ER) distribution. Various mathematical properties of the new model including ordinary and incomplete moment, quantile function, generating function are derived. We propose the method of maximum likelihood for estimating the model parameters. A real life data set is used to compare the flexibility of the new model with other models.

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