scholarly journals A Generalized Rayleigh Family of Distributions Based on the Modified Slash Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1226
Author(s):  
Inmaculada Barranco-Chamorro ◽  
Yuri A. Iriarte ◽  
Yolanda M. Gómez ◽  
Juan M. Astorga ◽  
Héctor W. Gómez
Keyword(s):  
Heavy Tails ◽  
Real Data ◽  
Rate Function ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Stochastic Representation ◽  
Likelihood Methods ◽  
Chi Square ◽  
Maximum Likelihood Methods ◽  
Family Of Distributions

Specifying a proper statistical model to represent asymmetric lifetime data with high kurtosis is an open problem. In this paper, the three-parameter, modified, slashed, generalized Rayleigh family of distributions is proposed. Its structural properties are studied: stochastic representation, probability density function, hazard rate function, moments and estimation of parameters via maximum likelihood methods. As merits of our proposal, we highlight as particular cases a plethora of lifetime models, such as Rayleigh, Maxwell, half-normal and chi-square, among others, which are able to accommodate heavy tails. A simulation study and applications to real data sets are included to illustrate the use of our results.

scholarly journals Burr X Exponential – G Family of Distributions: Properties and Application

2020 ◽  
pp. 58-75
Author(s):  
A. A. Sanusi ◽  
S. I. S. Doguwa ◽  
I. Audu ◽  
Y. M. Baraya
Keyword(s):  
Real Data ◽  
Moment Generating Function ◽  
Data Sets ◽  
Likelihood Methods ◽  
Positive Real ◽  
New Class ◽  
New Family ◽  
Maximum Likelihood Methods ◽  
Probability Weighted Moment ◽  
Family Of Distributions

In this paper, we developed a new class of continuous distributions called Burr X Exponential-G Family. Also, we obtained sub-models of this family of distributions such as Burr X Exponential-Rayleigh (BXE-R) and Burr X Exponential Lomax (BXE-Lx) distributions; by showing their respective densities functions. Some structural properties of the proposed family of distributions were derived such as moment, moment generating function, probability weighted moment, renyi entropy and order statistics. We estimate the parameters of the model by using Maximum Likelihood methods. Finally, the results obtained are validated using two real data sets. The results show that BXE-Lx distribution provides better fit in the data sets than some other well known distributions. However, this new family of distributions will serve as an additional generator for developing new sub models to modeling positive real data sets.

scholarly journals A Reliability Model Based on the Incomplete Generalized Integro-Exponential Function

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1537
Author(s):  
Juan M. Astorga ◽  
Jimmy Reyes ◽  
Karol I. Santoro ◽  
Osvaldo Venegas ◽  
Héctor W. Gómez
Keyword(s):  
Maximum Likelihood ◽  
Exponential Function ◽  
Real Data ◽  
Data Sets ◽  
Reliability Model ◽  
Likelihood Methods ◽  
Parameter Recovery ◽  
High Coefficient ◽  
Positive Data ◽  
Maximum Likelihood Methods

This article introduces an extension of the Power Muth (PM) distribution for modeling positive data sets with a high coefficient of kurtosis. The resulting distribution has greater kurtosis than the PM distribution. We show that the density can be represented based on the incomplete generalized integro-exponential function. We study some of its properties and moments, and its coefficients of asymmetry and kurtosis. We apply estimations using the moments and maximum likelihood methods and present a simulation study to illustrate parameter recovery. The results of application to two real data sets indicate that the new model performs very well in the presence of outliers.

scholarly journals A New Class of Distributions Generated by the Extended Bimodal-Normal Distribution

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Milton A. Cortés ◽  
David Elal-Olivero ◽  
Juan F. Olivares-Pacheco
Keyword(s):  
Monte Carlo Simulation ◽  
Normal Distribution ◽  
Real Data ◽  
Laplace Distribution ◽  
Data Sets ◽  
Stochastic Representation ◽  
New Class ◽  
New Family ◽  
Special Cases ◽  
Family Of Distributions

In this study, we present a new family of distributions through generalization of the extended bimodal-normal distribution. This family includes several special cases, like the normal, Birnbaum-Saunders, Student’s t, and Laplace distribution, that are developed and defined using stochastic representation. The theoretical properties are derived, and easily implemented Monte Carlo simulation schemes are presented. An inferential study is performed for the Laplace distribution. We end with an illustration of two real data sets.

scholarly journals Beta Kumaraswamy Burr Type X Distribution and Its Properties

2018 ◽  
Author(s):  
Umar Yusuf Madaki ◽  
Mohd Rizam Abu Bakar ◽  
Laba Handique
Keyword(s):  
Maximum Likelihood ◽  
Reliability Analysis ◽  
Real Data ◽  
Quantile Function ◽  
Model Parameters ◽  
Data Sets ◽  
Likelihood Methods ◽  
Proposed Model ◽  
Maximum Likelihood Methods ◽  
True Values

We proposed a so-called Beta Kumaraswamy Burr Type X distribution which gives the extension of the Kumaraswamy-G class of family distribution. Some properties of this proposed model were provided, like: the expansion of densities and quantile function. We considered the Bayes and maximum likelihood methods to estimate the parameters and also simulate the model parameters to validate the methods based on different set of true values. Some real data sets were employed to show the usefulness and flexibility of the model which serves as generalization to many sub-models in the field of engineering, medical, survival and reliability analysis.

scholarly journals Beta Kumaraswamy Burr Type X Distribution and Its Properties

2018 ◽  
Author(s):  
Umar Yusuf Madaki ◽  
Mohd Rizam Abu Bakar ◽  
Laba Handique
Keyword(s):  
Maximum Likelihood ◽  
Reliability Analysis ◽  
Real Data ◽  
Quantile Function ◽  
Model Parameters ◽  
Data Sets ◽  
Likelihood Methods ◽  
Proposed Model ◽  
Maximum Likelihood Methods ◽  
True Values

We proposed a so-called Beta Kumaraswamy Burr Type X distribution which gives the extension of the Kumaraswamy-G class of family distribution. Some properties of this proposed model were provided, like: the expansion of densi- ties and quantile function. We considered the Bayes and maximum likelihood methods to estimate the parameters and also simulate the model parameters to validate the methods based on dierent set of true values. Some real data sets were employed to show the usefulness and  exibility of the model which serves as generalization to many sub-models in the elds of engineering, medical, survival and reliability analysis.

scholarly journals THE POWER MUTH DISTRIBUTION∗

2017 ◽  
Vol 22 (2) ◽  
pp. 186-201 ◽  
Author(s):  
Pedro Jodra ◽  
Hector Wladimir Gomez ◽  
Maria Dolores Jimenez-Gamero ◽  
Maria Virtudes Alba-Fernandez
Keyword(s):  
Probability Distributions ◽  
Real Data ◽  
Rate Function ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Failure Rate Function ◽  
Monte Carlo Simulation Study ◽  
New Model ◽  
Practical Usefulness ◽  
Method Of Maximum Likelihood

Muth introduced a probability distribution with application in reliability theory. We propose a new model from the Muth law. This paper studies its statistical properties, such as the computation of the moments, computer generation of pseudo-random data and the behavior of the failure rate function, among others. The estimation of parameters is carried out by the method of maximum likelihood and a Monte Carlo simulation study assesses the performance of this method. The practical usefulness of the new model is illustrated by means of two real data sets, showing that it may provide a better fit than other probability distributions.

scholarly journals New General Transmuted Family of Distributions with Applications

2018 ◽  
pp. 807-829
Author(s):  
Md. Mahabubur Rahman ◽  
Bander Al-Zahrani ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
New Class ◽  
New Family ◽  
Family Of Distributions

In this paper, we have introduced a new family of general transmuted distributions and have studied the cubic transmuted family of distributions in detail. This new class of distributions oers more distributional exibility when bi-modality appear in the data sets. Some special members of the proposed cubic transmuted family of distributions have been discussed. We have investigated, in detail, the proposed cubic transmuted family of distributions for parent exponential distribution. The statistical properties along with the reliability behavior for the cubic transmuted exponential distribution have been studied. We have obtained the expressions for single and joint order statistics when a sample is available from the cubic transmuted exponential distribution. Maximum likelihood estimation of parameters for cubic transmuted exponential distribution has also been discussed. We have also discussed the simulation and real data applications of the proposed distribution.

scholarly journals Kumaraswamy Generalized Power Lomax Distributionand Its Applications

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 28-45
Author(s):  
Vasili B.V. Nagarjuna ◽  
R. Vishnu Vardhan ◽  
Christophe Chesneau
Keyword(s):  
Hazard Rate ◽  
Real Data ◽  
Rate Function ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
Parameter Distribution ◽  
Data Sets ◽  
Lomax Distribution ◽  
Entropy Measures ◽  
Modeling Behavior

In this paper, a new five-parameter distribution is proposed using the functionalities of the Kumaraswamy generalized family of distributions and the features of the power Lomax distribution. It is named as Kumaraswamy generalized power Lomax distribution. In a first approach, we derive its main probability and reliability functions, with a visualization of its modeling behavior by considering different parameter combinations. As prime quality, the corresponding hazard rate function is very flexible; it possesses decreasing, increasing and inverted (upside-down) bathtub shapes. Also, decreasing-increasing-decreasing shapes are nicely observed. Some important characteristics of the Kumaraswamy generalized power Lomax distribution are derived, including moments, entropy measures and order statistics. The second approach is statistical. The maximum likelihood estimates of the parameters are described and a brief simulation study shows their effectiveness. Two real data sets are taken to show how the proposed distribution can be applied concretely; parameter estimates are obtained and fitting comparisons are performed with other well-established Lomax based distributions. The Kumaraswamy generalized power Lomax distribution turns out to be best by capturing fine details in the structure of the data considered.

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 Theory and Applications of the Unit Gamma/Gompertz Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1850
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Rate Function ◽  
The Other ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Gompertz Distribution ◽  
Probability And Statistics ◽  
Analytical Behavior

Unit distributions are commonly used in probability and statistics to describe useful quantities with values between 0 and 1, such as proportions, probabilities, and percentages. Some unit distributions are defined in a natural analytical manner, and the others are derived through the transformation of an existing distribution defined in a greater domain. In this article, we introduce the unit gamma/Gompertz distribution, founded on the inverse-exponential scheme and the gamma/Gompertz distribution. The gamma/Gompertz distribution is known to be a very flexible three-parameter lifetime distribution, and we aim to transpose this flexibility to the unit interval. First, we check this aspect with the analytical behavior of the primary functions. It is shown that the probability density function can be increasing, decreasing, “increasing-decreasing” and “decreasing-increasing”, with pliant asymmetric properties. On the other hand, the hazard rate function has monotonically increasing, decreasing, or constant shapes. We complete the theoretical part with some propositions on stochastic ordering, moments, quantiles, and the reliability coefficient. Practically, to estimate the model parameters from unit data, the maximum likelihood method is used. We present some simulation results to evaluate this method. Two applications using real data sets, one on trade shares and the other on flood levels, demonstrate the importance of the new model when compared to other unit models.

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