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 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 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.

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.

scholarly journals Bayesian Estimation for Inverse Weibull Distribution Under Progressive Type-II Censored Data With Beta-Binomial Removals

2018 ◽  
Vol 47 (1) ◽  
pp. 77-94
Author(s):  
Pradeep Kumar Vishwakarma ◽  
Arun Kaushik ◽  
Aakriti Pandey ◽  
Umesh Singh ◽  
Sanjay Kumar Singh
Keyword(s):  
Weibull Distribution ◽  
Real Data ◽  
Estimation Procedure ◽  
Type Ii ◽  
Unknown Parameters ◽  
Data Set ◽  
Progressive Type ◽  
Inverse Weibull Distribution ◽  
Type Ii Censored Data ◽  
Censoring Scheme

This paper deals with the estimation procedure for inverse Weibull distribution under progressive type-II censored samples when removals follow Beta-binomial probability law. To estimate the unknown parameters, the maximum likelihood and Bayes estimators are obtained under progressive censoring scheme mentioned above. Bayes estimates are obtained using Markov chain Monte Carlo (MCMC) technique considering square error loss function and compared with the corresponding MLE's. Further, the expected total time on test is obtained under considered censoring scheme.  Finally, a real data set has been analysed to check the validity of the study.

scholarly journals THE BETA-WEIBULL DISTRIBUTION ON THE LATTICE OF INTEGERS

2016 ◽  
Vol 39 (1) ◽  
pp. 40 ◽  
Author(s):  
Vahid Nekoukhou ◽  
Hamid Bidram ◽  
Rasool Roozegar
Keyword(s):  
Weibull Distribution ◽  
Hazard Rate ◽  
Real Data ◽  
Rate Function ◽  
Discrete Analog ◽  
Discrete Distributions ◽  
Hazard Rate Function ◽  
Data Set ◽  
Beta Weibull Distribution ◽  
New Distribution

In this paper, a discrete analog of the beta-Weibull distribution is studied. This new distribution contains several discrete distributions as special sub-models. Some distributional and moment properties of the discrete beta-Weibull distribution as well as its order statistics are discussed. We will show that the hazard rate function of the new model can be increasing, decreasing, bathtub-shaped and upside-down bathtub. Estimation of the parameters is illustrated and the model with a real data set is also examined.

scholarly journals Weighted Version of Generalized Inverse Weibull Distribution

2019 ◽  
Vol 17 (2) ◽  
Author(s):  
Sofi Mudasir ◽  
S. P. Ahmad
Keyword(s):  
Weibull Distribution ◽  
Generalized Inverse ◽  
Real Life ◽  
Moment Generating Function ◽  
Weighted Version ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
Inverse Weibull Distribution ◽  
Better Than

Weighted distributions are used in many fields, such as medicine, ecology, and reliability. A weighted version of the generalized inverse Weibull distribution, known as weighted generalized inverse Weibull distribution (WGIWD), is proposed. Basic properties including mode, moments, moment generating function, skewness, kurtosis, and Shannon’s entropy are studied. The usefulness of the new model was demonstrated by applying it to a real-life data set. The WGIWD fits better than its submodels, such as length biased generalized inverse Weibull (LGIW), generalized inverse Weibull (GIW), inverse Weibull (IW) and inverse exponential (IE) distributions.

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