scholarly journals Mixture of Inverse Weibull and Lognormal Distributions: Properties, Estimation, and Illustration

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
K. S. Sultan ◽  
A. S. Al-Moisheer
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Component Mixture ◽  
Data Set ◽  
Hazard Functions ◽  
Lognormal Distributions ◽  
Proposed Model ◽  
Estimation Of Model Parameters

We discuss the two-component mixture of the inverse Weibull and lognormal distributions (MIWLND) as a lifetime model. First, we discuss the properties of the proposed model including the reliability and hazard functions. Next, we discuss the estimation of model parameters by using the maximum likelihood method (MLEs). We also derive expressions for the elements of the Fisher information matrix. Next, we demonstrate the usefulness of the proposed model by fitting it to a real data set. Finally, we draw some concluding remarks.

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 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 General Results for the Transmuted Family of Distributions and New Models

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Marcelo Bourguignon ◽  
Indranil Ghosh ◽  
Gauss M. Cordeiro
Keyword(s):  
Maximum Likelihood ◽  
Generating Functions ◽  
Real Data ◽  
Model Parameters ◽  
Data Set ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
The Family ◽  
New Models ◽  
Family Of Distributions

The transmuted family of distributions has been receiving increased attention over the last few years. For a baselineGdistribution, we derive a simple representation for the transmuted-Gfamily density function as a linear mixture of theGand exponentiated-Gdensities. We investigate the asymptotes and shapes and obtain explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean deviations, Rényi and Shannon entropies, and order statistics and their moments. We estimate the model parameters of the family by the method of maximum likelihood. We prove empirically the flexibility of the proposed model by means of an application to a real data set.

scholarly journals A New Generalized Weighted Weibull Distribution

2019 ◽  
pp. 161-178 ◽  
Author(s):  
Salman Abbas ◽  
Gamze Ozal ◽  
Saman Hanif Shahbaz ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Weibull Distribution ◽  
Generating Function ◽  
Probability Generating Function ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model

In this article, we present a new generalization of weighted Weibull distribution using Topp Leone family of distributions. We have studied some statistical properties of the proposed distribution including quantile function, moment generating function, probability generating function, raw moments, incomplete moments, probability, weighted moments, Rayeni and q th entropy. The have obtained numerical values of the various measures to see the eect of model parameters. Distribution of of order statistics for the proposed model has also been obtained. The estimation of the model parameters has been done by using maximum likelihood method. The eectiveness of proposed model is analyzed by means of a real data sets. Finally, some concluding remarks are given.

scholarly journals The complementary Poisson-Lindley class of distributions

2015 ◽  
Vol 3 (2) ◽  
pp. 146 ◽  
Author(s):  
Amal Hassan ◽  
Salwa Assar ◽  
Kareem Ali
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Formal Proof ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
Data Set ◽  
Lifetime Distributions ◽  
New Class ◽  
Rate Functions

<p>This paper proposed a new general class of continuous lifetime distributions, which is a complementary to the Poisson-Lindley family proposed by Asgharzadeh et al. [3]. The new class is derived by compounding the maximum of a random number of independent and identically continuous distributed random variables, and Poisson-Lindley distribution. Several properties of the proposed class are discussed, including a formal proof of probability density, cumulative distribution, and reliability and hazard rate functions. The unknown parameters are estimated by the maximum likelihood method and the Fisher’s information matrix elements are determined. Some sub-models of this class are investigated and studied in some details. Finally, a real data set is analyzed to illustrate the performance of new distributions.</p>

scholarly journals The Exponentiated Generalized Standardized Half-logistic Distribution

2017 ◽  
Vol 6 (3) ◽  
pp. 24 ◽  
Author(s):  
Gauss M. Cordeiro ◽  
Thiago A. N. De Andrade ◽  
Marcelo Bourguignon ◽  
Frank Gomes-Silva
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Data Set ◽  
Lorenz Curves ◽  
Lifetime Model ◽  
Two Parameter ◽  
New Distribution

We study a new two-parameter lifetime model called the exponentiated generalized standardized half-logistic distribution, which extends the half-logistic pioneered by Balakrishnan in the eighties. We provide explicit expressions for the moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves, and order statistics. The model parameters are estimated by the maximum likelihood method. A simulation study reveals that the estimators have desirable properties such as small biases and variances even in moderate sample sizes. We prove empirically that the new distribution provides a better fit to a real data set than other competitive 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.

scholarly journals The Transmuted Generalized Inverse Weibull Distribution

2014 ◽  
Vol 43 (2) ◽  
pp. 119-131 ◽  
Author(s):  
Faton Merovci ◽  
Ibrahim Elbatal ◽  
Alaa Ahmed
Keyword(s):  
Weibull Distribution ◽  
Generalized Inverse ◽  
Probability Distributions ◽  
Information Matrix ◽  
Real Data ◽  
Moment Generating Function ◽  
Model Parameters ◽  
Data Set ◽  
Method Of Maximum Likelihood ◽  
Inverse Weibull Distribution

A generalization of the generalized inverse Weibull distribution the so-called transmuted generalized inverse Weibull distribution is proposed and studied. We will use the quadratic rank transmutation map (QRTM) in order to generate a flexible family of probability distributions taking the generalized inverseWeibull distribution as the base value distribution by introducing a new parameter that would offer more distributional flexibility. Various structural properties including explicit expressions for the moments, quantiles, and moment generating function of the new distribution are derived. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set are used to compare the flexibility of the transmuted version versus the generalized inverse Weibull distribution.

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.

TWO SECTIONAL MODELS INVOLVING TWO WEIBULL DISTRIBUTIONS

1999 ◽  
Vol 06 (02) ◽  
pp. 103-122 ◽  
Author(s):  
RENYAN JIANG ◽  
MING J. ZUO ◽  
D. N. P. MURTHY
Keyword(s):  
Probability Density ◽  
Failure Rate ◽  
Real Data ◽  
Model Parameters ◽  
Weibull Distributions ◽  
Data Set ◽  
Failure Data ◽  
Rate Functions ◽  
Estimation Of Model Parameters

In this paper, we study two sectional models, each involving two Weibull distributions. Characterization of the plot on Weibull plotting paper (WPP) for each model is carried out. We also study the shapes of the probability density and the failure rate functions. These are useful in determining if a given failure data set can be modeled by such a model. We discuss the estimation of model parameters based on the WPP plot and illustrate through two examples involving real data.

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