scholarly journals The New Odd Log-Logistic Generalised Half-Normal Distribution: Mathematical Properties and Simulations

2019 ◽  
pp. 277-302 ◽  
Author(s):  
Mahmoud afshari Afshari ◽  
Mosa Abdi ◽  
Hamid Karamikabir ◽  
Mahdiye Mozafari ◽  
Morad Alizadeh
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Test Validity ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Moment Generating Function ◽  
Data Sets ◽  
Least Squares Estimators ◽  
Anderson Darling

The new distributions are very useful in describing real data sets, because these distributions are more flexible to model real data that present a high degree of skewness and kurtosis. The choice of the best-suited statistical distribution for modeling data is very important.In this paper, A new class of distributions called the {\it  New odd log-logistic generalized half-normal} (NOLL-GHN) family with four parameters is introduced and studied. This model contains  sub-models  such as  half-normal (HN), generalized half-normal (GHN )and odd log-logistic generalized half-normal (OLL-GHN) distributions.some statistical properties such as moments and moment generating function have been calculated.The Biases and MSE's of  estimator methods such as maximum likelihood estimators ,  least squares estimators, weighted least squares estimators,Cramer-von-Mises estimators, Anderson-Darling estimators and right tailed Anderson-Darling estimators  are calculated.The fitness capability of this model has been investigated  by fitting this model and others based on real data sets. The maximum likelihood  estimators are  assessed with simulated  real data from proposed model. We present the simulation in order to test validity of maximum likelihood estimators.

scholarly journals A New Generalized Odd Gamma Uniform Distribution: Mathematical Properties, Application and Simulation

2021 ◽  
Vol 20 ◽  
pp. 135-146
Author(s):  
B. Hossieni ◽  
M. Afshari ◽  
M. Alizadeh ◽  
H. Karamikabir
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Least Squares Estimators ◽  
Mathematical Properties ◽  
Anderson Darling ◽  
Von Mises ◽  
High Degree

n many applied areas there is a clear need for the extended forms of the well-known distributions.The new distributions are more flexible to model real data that present a high degree of skewness and kurtosis, such that each one solves a particular part of the classical distribution problems. In this paper, a new two-parameter Generalized Odd Gamma distribution, called the (GOGaU) distribution, is introduced and the fitness capability of this model are investigated. Some structural properties of the new distribution are obtained. The different methods including: Maximum likelihood estimators, Bayesian estimators (posterior mean and maximum a posterior), least squares estimators, weighted least squares estimators, Cramér-von-Mises estimators, Anderson-Darling and right tailed Anderson-Darling estimators are discussed to estimate the model parameters. In order to perform the applications, the importance and flexibility of the new model are also illustrated empirically by means of two real data sets. For simulation Stan and JAGS software were utilized in which we have built the GOGaU JAGS module

scholarly journals A New Three-Parameter Exponential Distribution with Variable Shapes for the Hazard Rate: Estimation and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 135 ◽  
Author(s):  
Ahmed Z. Afify ◽  
Osama Abdo Mohamed
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Sets ◽  
Least Squares Estimators ◽  
Mathematical Properties ◽  
Anderson Darling ◽  
Von Mises

In this paper, we study a new flexible three-parameter exponential distribution called the extended odd Weibull exponential distribution, which can have constant, decreasing, increasing, bathtub, upside-down bathtub and reversed-J shaped hazard rates, and right-skewed, left-skewed, symmetrical, and reversed-J shaped densities. Some mathematical properties of the proposed distribution are derived. The model parameters are estimated via eight frequentist estimation methods called, the maximum likelihood estimators, least squares and weighted least-squares estimators, maximum product of spacing estimators, Cramér-von Mises estimators, percentiles estimators, and Anderson-Darling and right-tail Anderson-Darling estimators. Extensive simulations are conducted to compare the performance of these estimation methods for small and large samples. Four practical data sets from the fields of medicine, engineering, and reliability are analyzed, proving the usefulness and flexibility of the proposed distribution.

scholarly journals The Generalized Odd Gamma-G Family of Distributions: Properties and Applications

2018 ◽  
Vol 47 (2) ◽  
pp. 69-89 ◽  
Author(s):  
Bistoon Hosseini ◽  
Mahmoud Afshari ◽  
Morad Alizadeh
Keyword(s):  
Maximum Likelihood ◽  
Test Validity ◽  
Estimation Method ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Data Sets ◽  
Maximum Likelihood Estimation Method ◽  
Family Of Distributions

Recently, new continuous distributions have been proposed to apply in statistical analysis. In this paper, the Generalized Odd Gamma-G distribution is introduced. In particular, G has been considered as the Uniform distribution and some statistical properties such as quantile function, asymptotics, moments, entropy and order statistics have been calculated.The fitness capability of this model has been investigated  by fitting this model and others based on real data sets. The  parameters of this model are estimated by the maximum likelihood estimation method with simulated  real data in order to test validity of maximum likelihood estimators .

Cubic Transmuted-G Family of Distributions and Its Properties

2018 ◽  
Vol 33 (2) ◽  
pp. 103-112 ◽  
Author(s):  
Muhammad Aslam ◽  
Zawar Hussain ◽  
Zahid Asghar
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Real Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Information Criteria ◽  
Data Sets ◽  
New Family ◽  
Family Of Distributions

Abstract In this article, a new family of distributions is introduced by using transmutation maps. The proposed family of distributions is expected to be useful in modeling real data sets. The genesis of the proposed family, including several statistical and reliability properties, is presented. Methods of estimation like maximum likelihood, least squares, weighted least squares, and maximum product spacing are discussed. Maximum likelihood estimation under censoring schemes is also considered. Further, we explore some special models of the proposed family of distributions and examined different properties of these special models. We compare three particular models of the proposed family with several existing distributions using different information criteria. It is observed that the proposed particular models perform better than different competing models. Applications of the particular models of the proposed family of distributions are finally presented to establish the applicability in real life situations.

scholarly journals Statistical Inferences on Odd Fréchet Power Function Distribution

2021 ◽  
Author(s):  
Muhammad Ahsan ul Haq ◽  
Mohammed Albassam ◽  
Muhammad Aslam ◽  
Sharqa Hashmi
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Real Data ◽  
Estimation Methods ◽  
Data Sets ◽  
Statistical Inferences ◽  
Proposed Model ◽  
Power Function Distribution ◽  
Anderson Darling ◽  
Von Mises

This article introduces a new unit distribution namely odd Fréchet power (OFrPF) distribution. Numerous properties of the proposed model including reliability analysis, moments, and Rényi Entropy for the proposed distribution. The parameters of the OFrPF distribution are obtained using different approaches such as maximum likelihood, least squares, weighted least squares, percentile, Cramer-von Mises, Anderson-Darling. Furthermore, a simulation was performed to study the performance of the suggested model. We also perform a simulation study to analyze the performances of estimation methods derived. The applications are used to show the practicality of OFrPF distribution using two real data sets. OFrPF distribution performed better than other competitive models.

scholarly journals Generalized Truncation Positive Normal Distribution

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1361
Author(s):  
Héctor J. Gómez ◽  
Diego I. Gallardo ◽  
Osvaldo Venegas
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Data Sets ◽  
New Model ◽  
Positive Support

In this article we study the properties, inference, and statistical applications to a parametric generalization of the truncation positive normal distribution, introducing a new parameter so as to increase the flexibility of the new model. For certain combinations of parameters, the model includes both symmetric and asymmetric shapes. We study the model’s basic properties, maximum likelihood estimators and Fisher information matrix. Finally, we apply it to two real data sets to show the model’s good performance compared to other models with positive support: the first, related to the height of the drum of the roller and the second, related to daily cholesterol consumption.

scholarly journals The Generalized Odd Generalized Exponential Fréchet Model: Univariate, Bivariate and Multivariate Extensions with Properties and Applications to the Univariate Version

2020 ◽  
pp. 529-544 ◽  
Author(s):  
Hisham Abdel Hamid Elsayed ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Generating Functions ◽  
Residual Life ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Simple Type ◽  
Data Sets ◽  
New Model ◽  
Clayton Copula ◽  
Stochastic Properties

A new univariate extension of the Fréchet distribution is proposed and studied. Some of its fundamental statistical properties such as stochastic properties, ordinary and incomplete moments, moments generating functions, residual life and reversed residual life functions, order statistics, quantile spread ordering, Rényi, Shannon and q-entropies are derived. A simple type Copula based construction using Morgenstern family and via Clayton Copula is employed to derive many bivariate and multivariate extensions of the new model. We assessed the performance of the maximum likelihood estimators using a simulation study. The importance of the new model is shown by means of two applications to real data sets.

scholarly journals A Novel Chen Extension: Theory, Characterizations and Different Estimation Methods

2021 ◽  
Vol 2 ◽  
pp. 1
Author(s):  
Haitham M. Yousof ◽  
Mustafa C. Korkmaz ◽  
G.G. Hamedani ◽  
Mohamed Ibrahim
Keyword(s):  
Numerical Analysis ◽  
Maximum Likelihood ◽  
Weighted Least Squares ◽  
Real Data ◽  
Estimation Methods ◽  
Simulation Studies ◽  
Data Set ◽  
Anderson Darling ◽  
Mean Variance ◽  
Skewness And Kurtosis

In this work, we derive a novel extension of Chen distribution. Some statistical properties of the new model are derived. Numerical analysis for mean, variance, skewness and kurtosis is presented. Some characterizations of the proposed distribution are presented. Different classical estimation methods under uncensored schemes such as the maximum likelihood, Anderson-Darling, weighted least squares and right-tail Anderson–Darling methods are considered. Simulation studies are performed in order to compare and assess the above-mentioned estimation methods. For comparing the applicability of the four classical methods, two application to real data set are analyzed.

scholarly journals A New Lindley-Burr XII Distribution: Model, Properties and Applications

2021 ◽  
Vol 10 (4) ◽  
pp. 33
Author(s):  
Boikanyo Makubate ◽  
Broderick Oluyede ◽  
Morongwa Gabanakgosi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Real Data ◽  
Distribution Model ◽  
Model Parameters ◽  
Data Sets ◽  
Mean Square ◽  
Conditional Moments ◽  
New Distribution

A new distribution called the Lindley-Burr XII (LBXII) distribution is proposed and studied. Some structural properties of the new distribution including moments, conditional moments, distribution of the order statistics and R´enyi entropy are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A simulation study to examine the bias and mean square error of the maximum likelihood estimators is presented and applications to real data sets in order to illustrate the usefulness of the new distribution are given.

scholarly journals The Odd Exponentiated Half-Logistic Exponential Distribution: Estimation Methods and Application to Engineering Data

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1684 ◽  
Author(s):  
Maha A. D. Aldahlan ◽  
Ahmed Z. Afify
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Exponential Distribution ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Model Parameters ◽  
Finite Sample ◽  
Anderson Darling ◽  
Von Mises ◽  
Cramer Von Mises

In this paper, we studied the problem of estimating the odd exponentiated half-logistic exponential (OEHLE) parameters using several frequentist estimation methods. Parameter estimation provides a guideline for choosing the best method of estimation for the model parameters, which would be very important for reliability engineers and applied statisticians. We considered eight estimation methods, called maximum likelihood, maximum product of spacing, least squares, Cramér–von Mises, weighted least squares, percentiles, Anderson–Darling, and right-tail Anderson–Darling for estimating its parameters. The finite sample properties of the parameter estimates are discussed using Monte Carlo simulations. In order to obtain the ordering performance of these estimators, we considered the partial and overall ranks of different estimation methods for all parameter combinations. The results illustrate that all classical estimators perform very well and their performance ordering, based on overall ranks, from best to worst, is the maximum product of spacing, maximum likelihood, Anderson–Darling, percentiles, weighted least squares, least squares, right-tail Anderson–Darling, and Cramér–von-Mises estimators for all the studied cases. Finally, the practical importance of the OEHLE model was illustrated by analysing a real data set, proving that the OEHLE distribution can perform better than some well known existing extensions of the exponential distribution.

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