scholarly journals Half-Logistic Xgamma Distribution: Properties and Estimation under Censored Samples

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Rashad Bantan ◽  
Amal S. Hassan ◽  
Mahmoud Elsehetry ◽  
B. M. Golam Kibria
Keyword(s):  
Maximum Likelihood ◽  
Residual Life ◽  
Stochastic Ordering ◽  
Real Data ◽  
Least Square ◽  
Likelihood Method ◽  
Mean Residual Life ◽  
Model Parameters ◽  
Censored Samples ◽  
Von Mises

This paper proposed a new probability distribution, namely, the half-logistic xgamma (HLXG) distribution. Various statistical properties, such as, moments, incomplete moments, mean residual life, and stochastic ordering of the proposed distribution, are discussed. Parameter estimation of the half-logistic xgamma distribution is approached by the maximum likelihood method based on complete and censored samples. Asymptotic confidence intervals of model parameters are provided. A simulation study is conducted to illustrate the theoretical results. Moreover, the model parameters of the HLXG distribution are estimated by using the maximum likelihood, least square, maximum product spacing, percentile, and Cramer–von Mises (CVM) methods. Superiority of the new model over some existing distributions is illustrated through three real data sets.

scholarly journals New Lindley Half Cauchy Distribution: Theory and Applications

2020 ◽  
Vol 9 (4) ◽  
pp. 1-7
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Cauchy Distribution ◽  
Least Square ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Set ◽  
Von Mises

In this paper, we have defined a new two-parameter new Lindley half Cauchy (NLHC) distribution using Lindley-G family of distribution which accommodates increasing, decreasing and a variety of monotone failure rates. The statistical properties of the proposed distribution such as probability density function, cumulative distribution function, quantile, the measure of skewness and kurtosis are presented. We have briefly described the three well-known estimation methods namely maximum likelihood estimators (MLE), least-square (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R software. By using the maximum likelihood method, we have constructed the asymptotic confidence interval for the model parameters. We verify empirically the potentiality of the new distribution in modeling a real data set.

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.

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 HALF LOGISTIC MODIFIED EXPONENTIAL DISTRIBUTION: PROPERTIES AND APPLICATIONS

2020 ◽  
pp. 276-287
Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar
Keyword(s):  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Least Square ◽  
Estimation Methods ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Type I ◽  
Data Set ◽  
Von Mises

In this study, we have introduced a three-parameter probabilistic model established from type I half logistic-Generating family called half logistic modified exponential distribution. The mathematical and statistical properties of this distribution are also explored. The behavior of probability density, hazard rate, and quantile functions are investigated. The model parameters are estimated using the three well known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE) and Cramer-Von-Mises estimation (CVME) methods. Further, we have taken a real data set and verified that the presented model is quite useful and more flexible for dealing with a real data set. KEYWORDS— Half-logistic distribution, Estimation, CVME ,LSE, , MLE

scholarly journals Lehmann Type II Frechet Poisson Distribution: Properties, Inference and Applications as a Life Time Distribution

2021 ◽  
Vol 10 (3) ◽  
pp. 8
Author(s):  
Adebisi Ade Ogunde ◽  
Gbenga Adelekan Olalude ◽  
Oyebimpe Emmanuel Adeniji ◽  
Kayode Balogun
Keyword(s):  
Maximum Likelihood ◽  
Poisson Distribution ◽  
Maximum Likelihood Method ◽  
Life Time ◽  
Real Data ◽  
Likelihood Method ◽  
Strength Parameter ◽  
Model Parameters ◽  
Type Ii ◽  
Time Data

A new generalization of the Frechet distribution called Lehmann Type II Frechet Poisson distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary moments, incomplete moments, generating functions, order statistics, Renyi entropy, stochastic ordering, Bonferroni and Lorenz curve, mean and median deviation, stress-strength parameter are investigated. The maximum likelihood method is used to estimate the model parameters. We examine the performance of the maximum likelihood method by means of a numerical simulation study. The new distribution is applied for modeling three real data sets to illustrate empirically its flexibility and tractability in modeling life time data.

scholarly journals The Beta Exponential Fréchet Distribution with Applications

2017 ◽  
Vol 46 (1) ◽  
pp. 41-63 ◽  
Author(s):  
M.E. Mead ◽  
Ahmed Z. Afify ◽  
G.G. Hamedani ◽  
Indranil Ghosh
Keyword(s):  
Residual Life ◽  
Real Data ◽  
Mean Residual Life ◽  
Model Parameters ◽  
Data Sets ◽  
Nested Models ◽  
Fréchet Distribution ◽  
Proposed Model ◽  
Mean Inactivity Time ◽  
Frechet Distribution

We define and study a new generalization of the Fréchet distribution called the beta exponential Fréchet distribution. The new model includes thirty two special models. Some of its mathematical properties, including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean residual life, mean inactivity time, order statistics and entropies are derived. The method of maximum likelihood is proposed to estimate the model parameters. A small simulation study is alsoreported. Two real data sets are applied to illustrate the flexibility of the proposed model compared with some nested and non-nested models.

scholarly journals A New Distribution for Modeling Lifetime Data with Different Methods of Estimation and Censored Regression Modeling

2020 ◽  
Vol 8 (2) ◽  
pp. 610-630 ◽  
Author(s):  
Mohamed Ibrahim ◽  
Emrah Altun EA ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Estimation Method ◽  
Least Square Method ◽  
Least Square ◽  
Likelihood Method ◽  
Survival Times ◽  
New Model ◽  
Von Mises ◽  
Bootstrapping Method

In this paper and after introducing a new model along with its properties, we estimate the unknown parameter of the new model using the Maximum likelihood method, Cram er-Von-Mises method, bootstrapping method, least square method and weighted least square method. We assess the performance of all estimation method employing simulations. All methods perform well but bootstrapping method is the best in modeling relief times whereas the maximum likelihood method is the best in modeling survival times. Censored data modeling with covariates is addressed along with the index plot of the modified deviance residuals and its Q-Q plot.

scholarly journals A Generalization of Binomial Exponential-2 Distribution: Copula, Properties and Applications

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1338
Author(s):  
Naif Alotaibi ◽  
Igor V. Malyk
Keyword(s):  
Residual Life ◽  
Real Life ◽  
Real Data ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Simple Type ◽  
Conditional Moment ◽  
Failure Rate Function ◽  
New Model

In this paper, we propose a new three-parameter lifetime distribution for modeling symmetric real-life data sets. A simple-type Copula-based construction is presented to derive many bivariate- and multivariate-type distributions. The failure rate function of the new model can be “monotonically asymmetric increasing”, “increasing-constant”, “monotonically asymmetric decreasing” and “upside-down-constant” shaped. We investigate some of mathematical symmetric/asymmetric properties such as the ordinary moments, moment generating function, conditional moment, residual life and reversed residual functions. Bonferroni and Lorenz curves and mean deviations are discussed. The maximum likelihood method is used to estimate the model parameters. Finally, we illustrate the importance of the new model by the study of real data applications to show the flexibility and potentiality of the new model. The kernel density estimation and box plots are used for exploring the symmetry of the used data.

scholarly journals Multivariate Skew-Power-Normal Distributions: Properties and Associated Inference

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1509
Author(s):  
Guillermo Martínez-Flórez ◽  
Artur J. Lemonte ◽  
Hugo S. Salinas
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Multivariate Distributions ◽  
Likelihood Approach ◽  
Information Matrices ◽  
Univariate Distribution

The univariate power-normal distribution is quite useful for modeling many types of real data. On the other hand, multivariate extensions of this univariate distribution are not common in the statistic literature, mainly skewed multivariate extensions that can be bimodal, for example. In this paper, based on the univariate power-normal distribution, we extend the univariate power-normal distribution to the multivariate setup. Structural properties of the new multivariate distributions are established. We consider the maximum likelihood method to estimate the unknown parameters, and the observed and expected Fisher information matrices are also derived. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. An empirical application of the proposed multivariate distribution to real data is provided for illustrative purposes.

scholarly journals The One-Parameter Odd Lindley Exponential Model: Mathematical Properties and Applications

2017 ◽  
Vol 32 (1) ◽  
Author(s):  
Mustafa Ç. Korkmaz ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Survival Data ◽  
Residual Life ◽  
Real Data ◽  
Exponential Model ◽  
Likelihood Method ◽  
Mean Squared Errors ◽  
Mathematical Properties ◽  
Data Application ◽  
The One

AbstractIn this article, an exponential model with only one shape parameter, which can be used in modeling survival data, reliability problems and fatigue life studies, is studied. We derive explicit expressions for some of its statistical and mathematical quantities including the ordinary moments, generating function, incomplete moments, order statistics, moment of residual life and reversed residual life. The model parameter is estimated by using the maximum likelihood method. A real data application is given to illustrate the flexibility of the model. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a simulation study.

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