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.

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.

Extended exponentiated Nadarajah-Haghighi model: Mathematical properties, characterizations and applications

2018 ◽  
Vol 55 (4) ◽  
pp. 498-522
Author(s):  
Morad Alizadeh ◽  
Mahdi Rasekhi ◽  
Haitham M. Yousof ◽  
Thiago G. Ramires ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Survival Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Rate Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Failure Rate Function ◽  
Data Set ◽  
Mathematical Properties

In this article, a new four-parameter model is introduced which can be used in mod- eling survival data and fatigue life studies. Its failure rate function can be increasing, decreasing, upside down and bathtub-shaped depending on its parameters. We derive explicit expressions for some of its statistical and mathematical quantities. Some useful characterizations are presented. Maximum likelihood method is used to estimate the model parameters. The censored maximum likelihood estimation is presented in the general case of the multi-censored data. We demonstrate empirically the importance and exibility of the new model in modeling a real data set.

scholarly journals The Odd Lindley-G Family of Distributions

2017 ◽  
Vol 46 (1) ◽  
pp. 65-87 ◽  
Author(s):  
Frank S. Gomes-Silva ◽  
Ana Percontini ◽  
Edleide de Brito ◽  
Manoel W. Ramos ◽  
Ronaldo Venâncio ◽  
...  
Keyword(s):  
Real Data ◽  
Quantile Function ◽  
Record Values ◽  
Model Parameters ◽  
Baseline Model ◽  
Data Set ◽  
New Family ◽  
Special Cases ◽  
Upper Record Values ◽  
Upper Record

We propose a new generator of continuous distributions with one extra positive parameter called the odd Lindley-G family. Some special cases are presented. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Various structural properties of the new family, which hold for any baseline model, are derived including explicit expressions for the quantile function, ordinary and incomplete moments, generating function, Renyi entropy, reliability, order statistics and their moments and k upper record values. We discuss estimation of the model parameters by maximum likelihood and provide an application to a real data set.

scholarly journals Validation of the Topp-Leone-Lomax Model via a Modified Nikulin-Rao-Robson Goodness-of-Fit Test with Different Methods of Estimation

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 57 ◽  
Author(s):  
Abhimanyu Singh Yadav ◽  
Hafida Goual ◽  
Refah Mohammed Alotaibi ◽  
Rezk H ◽  
M. Masoom Ali ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Rate Function ◽  
Estimation Methods ◽  
Model Parameters ◽  
Simple Type ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Failure Rate Function ◽  
New Model

In this paper, we introduce a new univariate version of the Lomax model as well as a simple type copula-based construction via Morgenstern family and via Clayton copula for introducing a new bivariate and a multivariate type extension of the new model. The new density has a strong physical interpretation and can be a symmetric function and unimodal with a heavy tail with positive skewness. The new failure rate function can be “upside-down”, “decreasing” with many different shapes and “decreasing-constant”. Some mathematical and statistical properties of the new model are derived. The model parameters are estimated using different estimation methods. For comparing the estimation methods, Markov Chain Monte Carlo (MCMC) simulations are performed. The applicability of the new model is illustrated via four real data applications, these data sets are symmetric and right skewed. We constructed a modified Chi-Square goodness-of-fit test based on Nikulin-Rao-Robson test in the case of complete and censored sample for the new model. Different simulation studies are performed along applications on real data for validation propose.

scholarly journals A Log-Beta Rayleigh Lomax Regression Model

2021 ◽  
Vol 16 (4) ◽  
pp. 2993-3007
Author(s):  
Nofiu Idowu Badmus ◽  
Mary Idowu Akinyemi ◽  
Josephine Nneamaka Onyeka-Ubaka
Keyword(s):  
Regression Model ◽  
Survival Data ◽  
Real Data ◽  
Model Parameters ◽  
Data Set ◽  
Cancer Data ◽  
Normal Probability ◽  
Method Of Maximum Likelihood ◽  
Classical Models ◽  
First Time

For the first time, a location-scale regression model based on the logarithm of an extended Raleigh Lomax distribution which has the ability to deal and model of any survival data than classical regression model is introduced. We obtain the estimate for the model parameters using the method of maximum likelihood by considering breast cancer data. In addition, normal probability plot of the residual is used to detect the outliers and evaluate model assumptions. We use a real data set to illustrate the performance of the new model, some of its submodels and classical models consider in the study. Also, we perform the statistics AIC, BIC and CAIC to select the most appropriate model among those regression models considered in the study.

scholarly journals A New Log-location Regression Model with Influence Diagnostics and Residual Analysis

2018 ◽  
pp. 417
Author(s):  
Emrah Altun ◽  
Haitham M. Yousof ◽  
GG Hamedani
Keyword(s):  
Regression Model ◽  
Estimation Method ◽  
Real Data ◽  
Distance Measures ◽  
Likelihood Method ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Data Set ◽  
Cook Distance ◽  
Influence Diagnostics

A new four-parameter lifetime model called OddLog-Logistic Burr XII distribution, is defined and investigated. Some of itsmathematical properties are derived. Some useful characterization resultsbased on \ the ratio of two truncated moments, based on the hazard functionas well as on the conditional expectation of certain functions of the randomvariable are presented. The maximum likelihood method is used to estimatethe model parameters by means of a graphical Monte Carlo simulation study.Moreover, we introduce a new log-location regression model based on theproposed distribution. The Jackknife estimation method as an alternativemethod is used to estimate the unknown parameters of new regression model. Thegeneralized cook distance and likelihood distance measures are used todetect the possible influential observations. The martingale and modifieddeviance residuals are defined to detect outliers and evaluate the modelassumptions. The potentiality of the new regression model is illustrated bymeans of a real data set.

scholarly journals The odd log-logistic gompertz lifetime distribution: Properties and applications

2019 ◽  
Vol 56 (1) ◽  
pp. 55-80
Author(s):  
Morad Alizadeh ◽  
Saeid Tahmasebi ◽  
Mohammad Reza Kazemi ◽  
Hamideh Siyamar Arabi Nejad ◽  
G. Hossein G. Hamedani
Keyword(s):  
Survival Data ◽  
Real Data ◽  
Rate Function ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Order Moment ◽  
Failure Rate Function ◽  
Data Set ◽  
Lifetime Distributions ◽  
New Distribution

Abstract In this paper, we introduce a new three-parameter generalized version of the Gompertz model called the odd log-logistic Gompertz (OLLGo) distribution. It includes some well-known lifetime distributions such as Gompertz (Go) and odd log-logistic exponential (OLLE) as special sub-models. This new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a decreasing, increasing and bathtub-shaped failure rate function depending on its parameters. Some mathematical properties of the new distribution, such as closed-form expressions for the density, cumulative distribution, hazard rate function, the kth order moment, moment generating function and the quantile measure are provided. We discuss maximum likelihood estimation of the OLLGo parameters as well as three other estimation methods from one observed sample. The flexibility and usefulness of the new distribution is illustrated by means of application to a real data set.

scholarly journals A New Generating Family of Distributions: Properties and Applications to the Weibull Exponential Model

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
El-Sayed A. El-Sherpieny ◽  
Salwa Assar ◽  
Tamer Helal
Keyword(s):  
Hazard Rate ◽  
Survival Function ◽  
Real Data ◽  
Exponential Model ◽  
Rate Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Set ◽  
Rate Functions ◽  
Family Of Distributions

A new method for generating family of distributions was proposed. Some fundamental properties of the new proposed family include the quantile, survival function, hazard rate function, reversed hazard and cumulative hazard rate functions are provided. This family contains several new models as sub models, such as the Weibull exponential model which was defined and discussed its properties. The maximum likelihood method of estimation is using to estimate the model parameters of the new proposed family. The flexibility and the importance of the Weibull-exponential model is assessed by applying it to a real data set and comparing it with other known models.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

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.

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