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 On the Burr XII-moment exponential distribution

PLoS ONE ◽  
2021 ◽  
Vol 16 (2) ◽  
pp. e0246935
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Mustafa Ç. Korkmaz ◽  
Wenhui Sheng ◽  
Azeem Ali
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Model Parameters ◽  
Simulation Studies ◽  
Conditional Moments ◽  
Mathematical Properties ◽  
Lifetime Model ◽  
Anderson Darling ◽  
Von Mises

In this study, a new flexible lifetime model called Burr XII moment exponential (BXII-ME) distribution is introduced. We derive some of its mathematical properties including the ordinary moments, conditional moments, reliability measures and characterizations. We employ different estimation methods such as the maximum likelihood, maximum product spacings, least squares, weighted least squares, Cramer-von Mises and Anderson-Darling methods for estimating the model parameters. We perform simulation studies on the basis of the graphical results to see the performance of the above estimators of the BXII-ME distribution. We verify the potentiality of the BXII-ME model via monthly actual taxes revenue and fatigue life applications.

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 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 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.

scholarly journals Weighted generalized Quasi Lindley distribution: Different methods of estimation, applications for Covid-19 and engineering data

2021 ◽  
Vol 6 (11) ◽  
pp. 11850-11878
Author(s):  
SidAhmed Benchiha ◽  
◽  
Amer Ibrahim Al-Omari ◽  
Naif Alotaibi ◽  
Mansour Shrahili ◽  
...  
Keyword(s):  
Least Squares ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Stochastic Ordering ◽  
Real Data ◽  
Ordinary Least Squares ◽  
Lifetime Distribution ◽  
Model Parameters ◽  
Lindley Distribution ◽  
Von Mises

<abstract><p>Recently, a new lifetime distribution known as a generalized Quasi Lindley distribution (GQLD) is suggested. In this paper, we modified the GQLD and suggested a two parameters lifetime distribution called as a weighted generalized Quasi Lindley distribution (WGQLD). The main mathematical properties of the WGQLD including the moments, coefficient of variation, coefficient of skewness, coefficient of kurtosis, stochastic ordering, median deviation, harmonic mean, and reliability functions are derived. The model parameters are estimated by using the ordinary least squares, weighted least squares, maximum likelihood, maximum product of spacing's, Anderson-Darling and Cramer-von-Mises methods. The performances of the proposed estimators are compared based on numerical calculations for various values of the distribution parameters and sample sizes in terms of the mean squared error (MSE) and estimated values (Es). To demonstrate the applicability of the new model, four applications of various real data sets consist of the infected cases in Covid-19 in Algeria and Saudi Arabia, carbon fibers and rain fall are analyzed for illustration. It turns out that the WGQLD is empirically better than the other competing distributions considered in this study.</p></abstract>

scholarly journals The Inverse-Power Logistic-Exponential Distribution: Properties, Estimation Methods, and Application to Insurance Data

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2060
Author(s):  
Mashail M. AL Sobhi
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Inverse Power ◽  
Model Parameters ◽  
Proposed Model ◽  
Anderson Darling ◽  
Von Mises ◽  
Insurance Data

The present paper proposes a new distribution called the inverse power logistic exponential distribution that extends the inverse Weibull, inverse logistic exponential, inverse Rayleigh, and inverse exponential distributions. The proposed model accommodates symmetrical, right-skewed, left-skewed, reversed-J-shaped, and J-shaped densities and increasing, unimodal, decreasing, reversed-J-shaped, and J-shaped hazard rates. We derive some mathematical properties of the proposed model. The model parameters were estimated using five estimation methods including the maximum likelihood, Anderson–Darling, least-squares, Cramér–von Mises, and weighted least-squares estimation methods. The performance of these estimation methods was assessed by a detailed simulation study. Furthermore, the flexibility of the introduced model was studied using an insurance real dataset, showing that the proposed model can be used to fit the insurance data as compared with twelve competing models.

scholarly journals The Complementary Exponentiated Lomax-Poisson Distribution with Applications to Bladder Cancer and Failure Data

2021 ◽  
Vol 50 (3) ◽  
pp. 77-105
Author(s):  
Devendra Kumar ◽  
Mazen Nassar ◽  
Ahmed Z. Afify ◽  
Sanku Dey
Keyword(s):  
Least Squares ◽  
Poisson Distribution ◽  
Weighted Least Squares ◽  
Real Data ◽  
Random Variable ◽  
Model Parameters ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
Failure Data ◽  
New Distribution

A new continuous four-parameter lifetime distribution is introduced by compounding the distribution of the maximum of a sequence of an independently identically exponentiated Lomax distributed random variables and zero truncated Poisson random variable, defined as the complementary exponentiated Lomax Poisson (CELP) distribution. The new distribution which exhibits decreasing and upside down bathtub shaped density while the distribution has the ability to model lifetime data with decreasing, increasing and upside-down bathtub shaped failure rates. The new distribution has a number of well-known lifetime special sub-models, such as Lomax-zero truncated Poisson distribution, exponentiated Pareto-zero truncated Poisson distribution and Pareto- zero truncated Poisson distribution. A comprehensive account of the mathematical and statistical properties of the new distribution is presented. The model parameters are obtained by the methods of maximum likelihood, least squares, weighted least squares, percentiles, maximum product of spacing and Cram\'er-von-Mises and compared them using Monte Carlo simulation study. We illustrate the performance of the proposed distribution by means of two real data sets and both the data sets show the new distribution is more appropriate as compared to the transmuted Lomax, beta exponentiated Lomax, McDonald Lomax, Kumaraswamy Lomax, Weibull Lomax, Burr X Lomax and Lomax distributions.

scholarly journals A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 440 ◽  
Author(s):  
Abdulhakim A. Al-babtain ◽  
I. Elbatal ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Simple Type ◽  
Data Sets ◽  
New Model ◽  
Clayton Copula ◽  
Mathematical Properties

In this article, we introduced a new extension of the binomial-exponential 2 distribution. We discussed some of its structural mathematical properties. A simple type Copula-based construction is also presented to construct the bivariate- and multivariate-type distributions. We estimated the model parameters via the maximum likelihood method. Finally, we illustrated the importance of the new model by the study of two real data applications to show the flexibility and potentiality of the new model in modeling skewed and symmetric data sets.

scholarly journals Reliability Properties of the NDL Family of Discrete Distributions with Its Inference

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1139
Author(s):  
Mohammed Mohammed Ahmed Almazah ◽  
Badr Alnssyan ◽  
Abdul Hadi N. Ahmed ◽  
Ahmed Z. Afify
Keyword(s):  
Least Squares ◽  
Negative Binomial ◽  
Weighted Least Squares ◽  
Sufficient Conditions ◽  
Real Life ◽  
Discrete Distributions ◽  
Real World Data ◽  
Life Problems ◽  
Anderson Darling ◽  
Von Mises

The natural discrete Lindley (NDL) distribution is an intuitive idea that uses discrete analogs to well-known continuous distributions rather than using any of the published discretization techniques. The NDL is a flexible extension of both the geometric and the negative binomial distributions. In the present article, we further investigate new results of value in the areas of both theoretical and applied reliability. To be specific, several closure properties of the NDL are proved. Among the results, sufficient conditions that maintain the preservation properties under useful partial orderings, convolution, and random sum of random variables are introduced. Eight different methods of estimation, including the maximum likelihood, least squares, weighted least squares, Cramér–von Mises, the maximum product of spacing, Anderson–Darling, right-tail Anderson–Darling, and percentiles, have been used to estimate the parameter of interest. The performance of these estimators has been evaluated through extensive simulation. We have also demonstrated two applications of NDL in modeling real-life problems, including count data. It is worth noting that almost all the methods have resulted in very satisfactory estimates on both simulated and real-world data.

Sign in / Sign up

Export Citation Format

Share Document