scholarly journals The Generalized Inverse Generalized Weibull Distribution and Its Properties

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Kanchan Jain ◽  
Neetu Singla ◽  
Suresh Kumar Sharma
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Mixture Model ◽  
Censored Data ◽  
Generalized Inverse ◽  
Weibull Distributions ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
Wide Range ◽  
Inverse Weibull Distribution

The Inverse Weibull distribution has been applied to a wide range of situations including applications in medicine, reliability, and ecology. It can also be used to describe the degradation phenomenon of mechanical components. We introduce Inverse Generalized Weibull and Generalized Inverse Generalized Weibull (GIGW) distributions. GIGW distribution is a generalization of several distributions in literature. The mathematical properties of this distribution have been studied and the mixture model of two Generalized Inverse Generalized Weibull distributions is investigated. Estimates of parameters using method of maximum likelihood have been computed through simulations for complete and censored data.

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 Extended Poisson Inverse Weibull Distribution: Theoretical and Computational Aspects

2019 ◽  
Vol 8 (2) ◽  
pp. 146
Author(s):  
Saeed Al-mualim
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Mathematical Properties ◽  
Inverse Weibull Distribution ◽  
Computational Aspects

A new extension of the Poisson Inverse Weibull distribution is derived and studied in details. Number of structural mathematical properties are derived. We used the well-known maximum likelihood method for estimating the model parameters. The new model is applied for modeling some real data sets to prove its importance and flexibility empirically.

The Poisson Nadarajah–Haghighi Distribution: Properties and Applications to Lifetime Data

2019 ◽  
Vol 27 (01) ◽  
pp. 2050005
Author(s):  
Muhammad Mansoor ◽  
M. H. Tahir ◽  
Aymaan Alzaatreh ◽  
Gauss M. Cordeiro
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Survival Data ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Lifetime Data ◽  
Monte Carlo Simulation Study ◽  
Mathematical Properties

A new three-parameter compounded extended-exponential distribution “Poisson Nadarajah–Haghighi” is introduced and studied, which is quite flexible and can be used effectively in modeling survival data. It can have increasing, decreasing, upside-down bathtub and bathtub-shaped failure rate. A comprehensive account of the mathematical properties of the model is presented. We discuss maximum likelihood estimation for complete and censored data. The suitability of the maximum likelihood method to estimate its parameters is assessed by a Monte Carlo simulation study. Four empirical illustrations of the new model are presented to real data and the results are quite satisfactory.

scholarly journals Box-Cox Gamma-G Family of Distributions: Theory and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1801
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Christophe Chesneau ◽  
Farrukh Jamal
Keyword(s):  
Maximum Likelihood ◽  
Statistical Model ◽  
Cauchy Distribution ◽  
Natural Generalization ◽  
Power Parameter ◽  
New Class ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
Box Cox Transformation ◽  
Family Of Distributions

This paper is devoted to a new class of distributions called the Box-Cox gamma-G family. It is a natural generalization of the useful Ristić–Balakrishnan-G family of distributions, containing a wide variety of power gamma-G distributions, including the odd gamma-G distributions. The key tool for this generalization is the use of the Box-Cox transformation involving a tuning power parameter. Diverse mathematical properties of interest are derived. Then a specific member with three parameters based on the half-Cauchy distribution is studied and considered as a statistical model. The method of maximum likelihood is used to estimate the related parameters, along with a simulation study illustrating the theoretical convergence of the estimators. Finally, two different real datasets are analyzed to show the fitting power of the new model compared to other appropriate models.

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.

scholarly journals Estimation of the Inverse Weibull Distribution Parameters under Type-I Hybrid Censoring

2021 ◽  
Vol 50 (5) ◽  
pp. 38-51
Author(s):  
Mohammad Kazemi ◽  
Mina Azizpoor
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Maximum Likelihood Estimates ◽  
Type I ◽  
Unknown Parameters ◽  
Bayes Estimates ◽  
Hybrid Censoring ◽  
Inverse Weibull Distribution ◽  
Distribution Parameters ◽  
Highest Posterior Density

The hybrid censoring is a mixture of type-I and type-II censoring schemes. This paper presents the statistical inferences of the inverse Weibull distribution parameters when the data are type-I hybrid censored. First, we consider the maximum likelihood estimates of the unknown parameters. It is observed that the maximum likelihood estimates can not be obtained in closed form. We further obtain the Bayes estimates and the corresponding highest posterior density credible intervals of the unknown parameters under the assumption of independent gamma priors using the importance sampling procedure. We also compute the approximate Bayes estimates using Lindley's approximation technique. The performance of the Bayes estimates have been compared with maximum likelihood estimates through the Monte Carlo Markov chain techniques. Finally, a real data set have been analysed for illustration purpose.

scholarly journals Comparative Study of Reliability of Some Antiseptic Soaps; A 3- Parameter Weibull Distribution

2015 ◽  
Vol 1 (01) ◽  
Author(s):  
Olubiyi O. A.
Keyword(s):  
Maximum Likelihood ◽  
Comparative Study ◽  
Weibull Distribution ◽  
Dissolution Time ◽  
Time To Failure ◽  
Likelihood Estimator ◽  
Method Of Maximum Likelihood ◽  
Mean And Variance ◽  
The Mean ◽  
Parameter Case

This study was carried out to estimate the dissolution time of some antiseptic soaps . The lifetime behavior of the antiseptic soaps was also modeled in order to estimate some basic measures and compare their lifetimes. In the analysis of data, the weibull distribution of 3-parameter case was used. The method of maximum likelihood estimator was used in estimating the parameters. The mean and variance time to failure, reliability, Weibull conditional reliability and Weibull reliable life of the products were obtained.

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