scholarly journals The Marshall–Olkin Generalized Inverse Weibull Distribution: Properties and Application

2019 ◽  
Vol 13 (2) ◽  
pp. 54
Author(s):  
Hamdy M. Salem
Keyword(s):  
Weibull Distribution ◽  
Hazard Function ◽  
Information Matrix ◽  
Real Data ◽  
Moment Generating Function ◽  
Least Square ◽  
Superior Performance ◽  
Inverse Weibull Distribution ◽  
Interval Estimators ◽  
New Distribution

In this paper, a new distribution namely, The Marshall–OlkinGeneralized Inverse Weibull Distribution is illustrated and studied. The new distribution is very flexible and contains sub-models such asinverse exponential, inverse Rayleigh, Weibull, inverse Weibull, Marshall–Olkininverse Weibull and Fréchetdistributions. Also, the hazard function of the new distribution can produce variety of forms:an increase, a decrease and an upside-down bathtub. Some properties such as hazard function, quintile function, entropy, moment generating function and order statistics are obtained. Different estimation approaches namely, maximum likelihood estimators, interval estimators, least square estimators, fisher information matrix and asymptotic confidence intervals are described. To illustrate the superior performance of the proposed distribution, a simulation study and a real data analysis are investigated against other models.

scholarly journals Different Classical Methods of Estimation and Chi-squared Goodness-of-fit Test for Unit Generalized Inverse Weibull Distribution

2021 ◽  
Vol 50 (5) ◽  
pp. 77-100
Author(s):  
Aidi khaoula ◽  
Sanku Dey ◽  
Devendra Kumar ◽  
Seddik-Ameur N
Keyword(s):  
Weibull Distribution ◽  
Simulation Study ◽  
Goodness Of Fit ◽  
Generalized Inverse ◽  
Real Data ◽  
Least Square ◽  
Data Set ◽  
Inverse Weibull Distribution ◽  
Chi Squared ◽  
New Distribution

In this paper, we try to contribute to the distribution theory literature by incorporating a new bounded distribution, called the unit generalized inverse Weibull distribution (UGIWD) in the (0, 1) intervals by transformation method. The proposed distribution exhibits  increasing and bathtub shaped hazard rate function. We derive some basic statistical properties of the new distribution. Based on complete sample, the model parameters are obtained by the methods of maximum likelihood, least square, weighted least square, percentile, maximum product of spacing and Cram`er-von-Mises and compared them using Monte Carlo simulation study. In addition, bootstrap confidence intervals of the parameters of the model based on aforementioned methods of estimation are also obtained. We illustrate the performance of the proposed distribution by means of one real data set and the data set shows that the new distribution is more appropriate as compared to unit Birnbaum-Saunders, unit gamma, unit Weibull, Kumaraswamy and unit Burr III distributions. Further, we construct chi-squared goodness-of-fit tests for the UGIWD using right censored data based on Nikulin-Rao-Robson (NRR) statistic and its modification. The criterion test used is the modified chi-squared statistic Y^2, developedby Bagdonavi?ius and Nikulin, 2011 for some parametric models when data are censored. The performances of the proposed test are shown by an intensive simulation study and an application to 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.

scholarly journals The Characterization of the Cubic Rank Inverse Weibull Distribution

2020 ◽  
pp. 20-33 ◽  
Author(s):  
Ogunde Adebisi Ade ◽  
Chukwu Angela Unna ◽  
Agwuegbo Samuel Obi-Nnamd
Keyword(s):  
Weibull Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Moment Generating Function ◽  
Data Set ◽  
Inverse Weibull Distribution ◽  
Maximum Likelihood Estimation Method ◽  
New Distribution

This work provides a new statistical distribution named Cubic rank transmuted Inverse Weibull distribution which was developed using the cubic transmutation map. Various statistical properties of the new distribution which includes: hazard function, moments, moment generating function, skewness, kurtosis, Renyl entropy and the order statistics were studied. A maximum likelihood estimation method was used in estimating the parameters of the distribution. Applications to real data set show the tractability of the distribution over other distributions and its sub-model.

Mathematical properties of the Kumaraswamy-Lindley distribution and its applications

2017 ◽  
Vol 5 (1) ◽  
pp. 17
Author(s):  
Hamdy Salem ◽  
Abd-Elwahab Hagag
Keyword(s):  
Hazard Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Least Square ◽  
Estimation Of Parameters ◽  
Least Square Estimation ◽  
Mathematical Properties ◽  
Composite Distribution

In this paper, a composite distribution of Kumaraswamy and Lindley distributions namely, Kumaraswamy-Lindley Kum-L distribution is introduced and studied. The Kum-L distribution generalizes sub-models for some widely known distributions. Some mathematical properties of the Kum-L such as hazard function, quantile function, moments, moment generating function and order statistics are obtained. Estimation of parameters for the Kum-L using maximum likelihood estimation and least square estimation techniques are provided. To illustrate the usefulness of the proposed distribution, simulation study and real data example are used.

scholarly journals The Half-Logistic Generalized Weibull Distribution

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Masood Anwar ◽  
Amna Bibi
Keyword(s):  
Weibull Distribution ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Type I ◽  
Failure Rate Function ◽  
New Model ◽  
Compound Distribution

A new three-parameter generalized distribution, namely, half-logistic generalized Weibull (HLGW) distribution, is proposed. The proposed distribution exhibits increasing, decreasing, bathtub-shaped, unimodal, and decreasing-increasing-decreasing hazard rates. The distribution is a compound distribution of type I half-logistic-G and Dimitrakopoulou distribution. The new model includes half-logistic Weibull distribution, half-logistic exponential distribution, and half-logistic Nadarajah-Haghighi distribution as submodels. Some distributional properties of the new model are investigated which include the density function shapes and the failure rate function, raw moments, moment generating function, order statistics, L-moments, and quantile function. The parameters involved in the model are estimated using the method of maximum likelihood estimation. The asymptotic distribution of the estimators is also investigated via Fisher’s information matrix. The likelihood ratio (LR) test is used to compare the HLGW distribution with its submodels. Some applications of the proposed distribution using real data sets are included to examine the usefulness of the distribution.

scholarly journals New Distribution for Fitting Discrete Data: The Poisson-Gold Distribution and Its Statistical Properties

2021 ◽  
Vol 50 (4) ◽  
pp. 19-35
Author(s):  
Ahmad Hanandeh ◽  
Amjad D. Al-Nasser
Keyword(s):  
Method Of Moments ◽  
Real Data ◽  
Moment Generating Function ◽  
Lifetime Distribution ◽  
Superior Performance ◽  
Lifetime Distributions ◽  
Practical Applications ◽  
Mathematical Properties ◽  
Distribution Parameters ◽  
New Distribution

Motivated mainly by lifetime issues, a new lifetime distribution coined ``Discrete Poisson-Gold distribution'' is introduced in this paper. Different structural properties of the new distribution are derived including moment generating function and the $r^{th}$ moment and others are presented. In addition, we discussed various important mathematical properties of the new distribution including estimation procedures for estimating the distribution parameters using the maximum likelihood and method of moments. The usefulness and credibility of the distribution are illustrated by means of two real-data applications to show its superior performance over some other well-known lifetime distributions and to prove its versatility in practical applications.

scholarly journals Lomax-Gumbel {Fréchet}: A New Distribution

2019 ◽  
pp. 1-19
Author(s):  
M. R. Mahmoud ◽  
R. M. Mandouh ◽  
R. E. Abdelatty
Keyword(s):  
Generating Function ◽  
Simulation Study ◽  
Hazard Function ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Data Sets ◽  
Function Estimate ◽  
Frechet Distribution ◽  
New Distribution

In this paper the T-R{Y} framework is used for proposing a new distribution that called The Lomax-Gumbel{Frechet} distribution. We study in details the properties of this distribution including hazard function, quantile Function, the skewness, the kurtosis, transformation, Renyi entropy, and moment generating function. Estimate of the parameters will be obtained using the MLE method. We present a simulation study and t the distribution to two real data sets.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

scholarly journals Transmuted Weibull distribution and its applications

2018 ◽  
Vol 157 ◽  
pp. 08007 ◽  
Author(s):  
Ivana Pobočíková ◽  
Zuzana Sedliačková ◽  
Mária Michalková
Keyword(s):  
Weibull Distribution ◽  
Real Data ◽  
Data Set ◽  
New Distribution ◽  
Modelling Data

In this paper we study new distribution called transmuted Weibull distribution. Some properties of this distribution are described. The usefulness of the distribution for modelling data is illustrated using real data set.

scholarly journals Brand Awareness via Online Media: An Evidence Using Instagram Medium with Statistical Analysis

2022 ◽  
Vol 2022 ◽  
pp. 1-13
Author(s):  
Mi Yantian ◽  
Zubair Ahmad ◽  
Ibrahim Alkhairy ◽  
Hassan Alsuhabi ◽  
Morad Alizadeh ◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Generalized Inverse ◽  
Statistical Tests ◽  
Weibull Model ◽  
Estimation Methods ◽  
Online Media ◽  
Mathematical Treatment ◽  
Family Approach ◽  
Inverse Weibull Distribution ◽  
New Distribution

Online marketing refers to the practices of promoting a company’s brand to its potential customers. It helps the companies to find new venues and trade worldwide. Numerous online media such as Facebook, YouTube, Twitter, and Instagram are available for marketing to promote and sell a company’s product. However, in this study, we use Instagram as a marketing medium to see its impact on sales. To carry out the computational process, the approach of linear regression modeling is adopted. Certain statistical tests are implemented to check the significance of Instagram as a marketing tool. Furthermore, a new statistical model, namely a new generalized inverse Weibull distribution, is introduced. This model is obtained using the inverse Weibull model with the new generalized family approach. Certain mathematical properties of the new generalized inverse Weibull model such as moments, order statistics, and incomplete moments are derived. A complete mathematical treatment of the heavy-tailed characteristics of the new generalized inverse Weibull distribution is also provided. Different estimation methods are discussed to obtain the estimators of the new model. Finally, the applicability of the new generalized inverse Weibull model is established via analyzing Instagram advertising data. The comparison of the new distribution is made with two other models. Based on seven analytical tools, it is observed that the new distribution is a better model to deal with data in the business, finance, and management sectors.

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