scholarly journals Bounded Odd Inverse Pareto Exponential Distribution: Properties, Estimation, and Regression

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Suleman Nasiru ◽  
Abdul Ghaniyyu Abubakari ◽  
Irene Dekomwine Angbing
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Regression Model ◽  
Exponential Distribution ◽  
Rate Function ◽  
Unit Interval ◽  
Parameter Distribution ◽  
Failure Rate Function ◽  
Response Variable ◽  
New Distribution

In this paper, we introduce a new three-parameter distribution defined on the unit interval. The density function of the distribution exhibits different kinds of shapes such as decreasing, increasing, left skewed, right skewed, and approximately symmetric. The failure rate function shows increasing, bathtub, and modified upside-down bathtub shapes. Six different frequentist estimation procedures were proposed for estimating the parameters of the distribution and their performance assessed via Monte Carlo simulations. Applications of the distribution were illustrated by analyzing two datasets and its fit compared to that of other distributions defined on the unit interval. Finally, we developed a regression model for a response variable that follows the new distribution.

scholarly journals Sinh Inverted Exponential Distribution: Simulation & Application to Neck Cancer Disease

2020 ◽  
Vol 9 (5) ◽  
pp. 11
Author(s):  
Saeed E. Hemeda ◽  
Ali M. Abdallah
Keyword(s):  
Exponential Distribution ◽  
Neck Cancer ◽  
Moment Generating Function ◽  
Rate Function ◽  
Residual Lifetime ◽  
Failure Rate Function ◽  
Cancer Disease ◽  
Asymptotic Expressions ◽  
Mean Residual Lifetime ◽  
New Distribution

A goal of this research is providing new probability distribution called Sinh inverted exponential distribution. The new distribution was extensively depending on the hyperbolic sine family of distributions with exponential distribution as a baseline distribution. Valuable statistical properties of the proposed distribution including mathematical and asymptotic expressions for its probability density function and Reliability. Moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics and entropies are derived. Actually, the applicability and validation of this model is proved in simulation study and an application to neck cancer disease data.

scholarly journals New Method for Generating New Families of Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 726
Author(s):  
Lamya A. Baharith ◽  
Wedad H. Aljuhani
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Rate Function ◽  
New Method ◽  
Likelihood Method ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Failure Rate Function ◽  
New Approach ◽  
Numerical Studies

This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this distribution can take asymmetric and near-symmetric shapes. Various asymmetric shapes, such as decreasing, increasing, L-shaped, near-symmetrical, and right-skewed shapes, are observed for the related failure rate function, making it more tractable for many modeling applications. Some significant mathematical features of the suggested distribution are determined. Estimates of the unknown parameters of the proposed distribution are obtained using the maximum likelihood method. Furthermore, some numerical studies were carried out, in order to evaluate the estimation performance. Three practical datasets are considered to analyze the usefulness and flexibility of the introduced distribution. The proposed alpha power Weibull–exponential distribution can outperform other well-known distributions, showing its great adaptability in the context of real data analysis.

scholarly journals Bayesian and Classical Inference under Type-II Censored Samples of the Extended Inverse Gompertz Distribution with Engineering Applications

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1578
Author(s):  
Ahmed Elshahhat ◽  
Hassan M. Aljohani ◽  
Ahmed Z. Afify
Keyword(s):  
Real Life ◽  
Rate Function ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Alpha Power ◽  
Type Ii ◽  
Failure Rate Function ◽  
Censored Samples ◽  
Inverse Gamma ◽  
Bathtub Shape

In this article, we introduce a new three-parameter distribution called the extended inverse-Gompertz (EIGo) distribution. The implementation of three parameters provides a good reconstruction for some applications. The EIGo distribution can be seen as an extension of the inverted exponential, inverse Gompertz, and generalized inverted exponential distributions. Its failure rate function has an upside-down bathtub shape. Various statistical and reliability properties of the EIGo distribution are discussed. The model parameters are estimated by the maximum-likelihood and Bayesian methods under Type-II censored samples, where the parameters are explained using gamma priors. The performance of the proposed approaches is examined using simulation results. Finally, two real-life engineering data sets are analyzed to illustrate the applicability of the EIGo distribution, showing that it provides better fits than competing inverted models such as inverse-Gompertz, inverse-Weibull, inverse-gamma, generalized inverse-Weibull, exponentiated inverted-Weibull, generalized inverted half-logistic, inverted-Kumaraswamy, inverted Nadarajah–Haghighi, and alpha-power inverse-Weibull distributions.

scholarly journals Maximum Likelihood and Two-Step Estimation of an Ordered-Probit Selection Model

2007 ◽  
Vol 7 (2) ◽  
pp. 167-182 ◽  
Author(s):  
Richard Chiburis ◽  
Michael Lokshin
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Monte Carlo Simulations ◽  
Regression Model ◽  
Selection Rule ◽  
Ordered Probit ◽  
Maximum Likelihood Estimates ◽  
Full Information ◽  
Full Information Maximum Likelihood ◽  
Two Step Estimation

We discuss the estimation of a regression model with an ordered-probit selection rule. We have written a Stata command, oheckman, that computes two-step and full-information maximum-likelihood estimates of this model. Using Monte Carlo simulations, we compare the performances of these estimators under various conditions.

scholarly journals One-Parameter Weibull-Type Distribution, Its Relative Entropy with Respect to Weibull and a Fractional Two-Parameter Exponential Distribution

Stats ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 34-54
Author(s):  
Aris Alexopoulos
Keyword(s):  
Exponential Distribution ◽  
Relative Entropy ◽  
Real Data ◽  
Parameter Distribution ◽  
Sample Mean ◽  
Type Distribution ◽  
Two Parameter ◽  
New Distribution ◽  
Extra Parameter ◽  
Mathematical Characteristics

A new one-parameter distribution is presented with similar mathematical characteristics to the two parameter conventional Weibull. It has an estimator that only depends on the sample mean. The relative entropy with respect to the Weibull distribution is derived in order to examine the level of similarity between them. The performance of the new distribution is compared to the Weibull and in some cases the Gamma distribution using real data. In addition, the Exponential distribution is modified to include an extra parameter via a simple transformation using fractional mathematics. It will be shown that the modified version also exhibits Weibull characteristics for particular values of the second parameter.

scholarly journals A New Extension of Lindley Geometric Distribution and its Applications

2019 ◽  
pp. 249-263
Author(s):  
I. Elbatal ◽  
Mohamed G. Khalil
Keyword(s):  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Geometric Distribution ◽  
Real Data ◽  
Rate Function ◽  
Likelihood Method ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Data Set ◽  
New Distribution

A new four-parameter distribution called the beta Lindley-geometric distribution is proposed. The hazard rate function of the new model can be constant, decreasing, increasing, upside down bathtub or bathtub failure rate shapes. Various structural properties including of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated using a real data set.

scholarly journals On the Arcsecant Hyperbolic Normal Distribution. Properties, Quantile Regression Modeling and Applications

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 117 ◽  
Author(s):  
Mustafa Ç. Korkmaz ◽  
Christophe Chesneau ◽  
Zehra Sedef Korkmaz
Keyword(s):  
Quantile Regression ◽  
Regression Model ◽  
Normal Distribution ◽  
Order Statistics ◽  
Random Variable ◽  
Unit Interval ◽  
Parametric Estimation ◽  
Simulation Studies ◽  
Quantile Regression Model ◽  
New Distribution

This work proposes a new distribution defined on the unit interval. It is obtained by a novel transformation of a normal random variable involving the hyperbolic secant function and its inverse. The use of such a function in distribution theory has not received much attention in the literature, and may be of interest for theoretical and practical purposes. Basic statistical properties of the newly defined distribution are derived, including moments, skewness, kurtosis and order statistics. For the related model, the parametric estimation is examined through different methods. We assess the performance of the obtained estimates by two complementary simulation studies. Also, the quantile regression model based on the proposed distribution is introduced. Applications to three real datasets show that the proposed models are quite competitive in comparison to well-established models.

scholarly journals Estimation Methods of Alpha Power Exponential Distribution with Applications to Engineering and Medical Data

2020 ◽  
pp. 149-166 ◽  
Author(s):  
Mazen Nassar ◽  
Ahmed Z. Afify ◽  
Mohammed Shakhatreh
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Exponential Distribution ◽  
Real Data ◽  
Medical Data ◽  
Estimation Methods ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Data Set ◽  
Distribution Parameters

This paper addresses the estimation of the unknown parameters of the alphapower exponential distribution (Mahdavi and Kundu, 2017) using nine frequentist estimation methods. We discuss the nite sample properties of the parameterestimates of the alpha power exponential distribution via Monte Carlo simulations. The potentiality of the distribution is analyzed by means of two real datasets from the elds of engineering and medicine. Finally, we use the maximumlikelihood method to derive the estimates of the distribution parameters undercompeting risks data and analyze one real data set.

scholarly journals A New Lifetime Model: Copulas, Properties and Real Lifetime Data Applications

2021 ◽  
pp. 195-211
Author(s):  
Wahid Shehata
Keyword(s):  
Maximum Likelihood ◽  
Rate Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Finite Sample ◽  
Failure Rate Function ◽  
Failure Times ◽  
Lifetime Model ◽  
New Distribution

A new four parameter lifetime model called the Weibullgeneralized Lomax is proposed and studied.  The new density function can be "right skewed", "symmetric" and "left skewed" and its corresponding failure rate function can be "monotonically decreasing", " monotonically increasing" and "constant". The skewness of the new distribution can negative and positive. The maximum likelihood method is employed and used for estimating the model parameters. Using the "biases" and "mean squared errors", we performed simulation experiments for assessing the finite sample behavior of the maximum likelihood estimators. The new model deserved to be chosen as the best model among many well-known Lomax extension such as exponentiated Lomax, gamma Lomax, Kumaraswamy Lomax, odd log-logistic Lomax, Macdonald Lomax, beta Lomax, reduced odd log-logistic Lomax, reduced Burr-Hatke Lomax, reduced WG-Lx, special generalized mixture Lomax and the standard Lomax distributions in modeling the "failure times" and the "service times" data sets.

The beta generalized half-normal geometric distribution

2013 ◽  
Vol 50 (4) ◽  
pp. 523-554 ◽  
Author(s):  
Thiago Ramires ◽  
Edwin Ortega ◽  
Gauss Cordeiro ◽  
Gholamhoss Hamedani
Keyword(s):  
Regression Model ◽  
Geometric Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Rate Function ◽  
Model Parameters ◽  
Normal Density ◽  
Simple Relationship ◽  
Failure Rate Function ◽  
Data Set

The beta generalized half-normal distribution is commonly used to model lifetimes. We propose a new wider distribution called the beta generalized half-normal geometric distribution, whose failure rate function can be decreasing, increasing or upside-down bathtub. Its density function can be expressed as a linear combination of beta generalzed half-normal density functions. We derive quantile function, moments and generating unction. We characterize the proposed distribution using a simple relationship between wo truncated moments. The method of maximum likelihood is adapted to estimate the model parameters and its potentiality is illustrated with an application to a real fatigue data set. Further, we propose a new extended regression model based on the logarithm of the new distribution. This regression model can be very useful for the analysis of real data and provide more realistic fits than other special regression models.

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