scholarly journals On the Discrete Weibull Marshall–Olkin Family of Distributions: Properties, Characterizations, and Applications

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 287
Author(s):  
Jiju Gillariose ◽  
Oluwafemi Samson Balogun ◽  
Ehab M. Almetwally ◽  
Rehan Ahmad Khan Sherwani ◽  
Farrukh Jamal ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Confidence Intervals ◽  
Geometric Distribution ◽  
Exponential Model ◽  
Parameters Estimation ◽  
Estimation Methods ◽  
Mathematical Properties ◽  
Discrete Family ◽  
Special Case ◽  
Family Of Distributions

In this article, we introduce a new flexible discrete family of distributions, which accommodates wide collection of monotone failure rates. A sub-model of geometric distribution or a discrete generalization of the exponential model is proposed as a special case of the derived family. Besides, we point out a comprehensive record of some of its mathematical properties. Two distinct estimation methods for parameters estimation and two different methods for constructing confidence intervals are explored for the proposed distribution. In addition, three extensive Monte Carlo simulations studies are conducted to assess the advantages between estimation methods. Finally, the utility of the new model is embellished by dint of two real datasets.

scholarly journals The Generalized Transmuted Poisson-G Family of Distributions: Theory, Characterizations and Applications

2018 ◽  
pp. 759-779 ◽  
Author(s):  
Haitham Yousof ◽  
Ahmed Z Afify ◽  
Morad Alizadeh ◽  
G. G. Hamedani ◽  
S. Jahanshahi ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Order Statistics ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Continuous Distributions ◽  
New Class ◽  
Mathematical Properties ◽  
Family Of Distributions

In this work, we introduce a new class of continuous distributions called the generalized poissonfamily which extends the quadratic rank transmutation map. We provide some special models for thenew family. Some of its mathematical properties including Rényi and q-entropies, order statistics andcharacterizations are derived. The estimations of the model parameters is performed by maximumlikelihood method. The Monte Carlo simulations is used for assessing the performance of the maximumlikelihood estimators. The ‡exibility of the proposed family is illustrated by means of two applicationsto real data sets.

scholarly journals A New Generalized Weibull- Odd Frѐchet Family of Distributions: Statistical Properties and Applications

2020 ◽  
pp. 25-43
Author(s):  
A. Usman ◽  
S. I. S. Doguwa ◽  
B. B. Alhaji ◽  
A. T. Imam
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Order Statistics ◽  
Mean Squared Error ◽  
Moment Generating Function ◽  
Data Sets ◽  
Mathematical Properties ◽  
Squared Error ◽  
New Distribution ◽  
Family Of Distributions

We introduced a new generalized Weibull- Odd Frѐchet family of distributions with three extra parameters and we derived some of its structural properties. We derived comprehensive mathematical properties which include moments, moment generating function, Entropies and Order Statistics. One family of this distribution called new generalized Weibull- Odd Frѐchet -Frѐchet distribution is used to fit two data sets using the MLE procedure. A Monte Carlo simulation is used to test the robustness of the parameters of this distribution, in terms of the bias and mean squared error. The results of fitting this new distribution to two different data sets suggest that the new distribution outperforms its competitors.

scholarly journals The Analysis for the Recovery Cases of COVID-19 in Egypt using Odd Generalized Exponential Lomax Distribution

2021 ◽  
pp. 52-65
Author(s):  
Hanem Mohamed ◽  
Amina E. Abo-Hussien ◽  
Salwa A. Mousa ◽  
Magda M. Ismail
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Confidence Intervals ◽  
The Other ◽  
Model Parameters ◽  
Practical Applications ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Asymptotic Confidence Intervals

In this paper, an odd generalized exponential Lomax (OGEL, in short) distribution has been considered. Some mathematical properties of the distribution are studied. The methods of maximum likelihood and maximum product of spacing are used for estimating the model parameters.  Moreover, 95% asymptotic confidence intervals for the estimates of the parameters are derived. The Monte Carlo simulation is conducted for the two proposed methods of estimation to evaluate the performance of the various proposed estimators. The proposed methods are utilized to find estimates of the parameters of OGEL distribution for the daily recovery cases of COIVD-19 in Egypt from 12 May to 30 September 2020.The practical applications show that the proposed model provides better fits than the other models.

scholarly journals On dynamic mutual information for bivariate lifetimes

2015 ◽  
Vol 47 (4) ◽  
pp. 1157-1174 ◽  
Author(s):  
Jafar Ahmadi ◽  
Antonio Di Crescenzo ◽  
Maria Longobardi
Keyword(s):  
Mutual Information ◽  
Order Statistics ◽  
Random Sample ◽  
Exponential Model ◽  
Multicomponent Systems ◽  
Distribution Free ◽  
Lifetime Distributions ◽  
Different Ages ◽  
Special Case ◽  
Residual Lifetimes

We consider dynamic versions of the mutual information of lifetime distributions, with a focus on past lifetimes, residual lifetimes, and mixed lifetimes evaluated at different instants. This allows us to study multicomponent systems, by measuring the dependence in conditional lifetimes of two components having possibly different ages. We provide some bounds, and investigate the mutual information of residual lifetimes within the time-transformed exponential model (under both the assumptions of unbounded and truncated lifetimes). Moreover, with reference to the order statistics of a random sample, we evaluate explicitly the mutual information between the minimum and the maximum, conditional on inspection at different times, and show that it is distribution-free in a special case. Finally, we develop a copula-based approach aiming to express the dynamic mutual information for past and residual bivariate lifetimes in an alternative way.

scholarly journals Implementation of strain-life fatigue parameters estimation methods in a web-based system

2011 ◽  
Vol 10 ◽  
pp. 2363-2368 ◽  
Author(s):  
Robert Basan ◽  
Marina Franulovic ◽  
Domagoj Rubeša ◽  
Ivan Prebil
Keyword(s):  
Parameters Estimation ◽  
Estimation Methods ◽  
Web Based ◽  
Web Based System

scholarly journals Estimating the Parameters of the Exponential-Geometric distribution based on progressively type-II censored data

2018 ◽  
Vol 6 (1) ◽  
pp. 37
Author(s):  
Aisha Fayomi ◽  
Hamdah Al-Shammari
Keyword(s):  
Censored Data ◽  
Geometric Distribution ◽  
Asymptotic Variance ◽  
Parameters Estimation ◽  
Type Ii ◽  
Progressive Type ◽  
The Em Algorithm ◽  
Asymptotic Confidence Intervals ◽  
Distribution Parameters ◽  
Type Ii Censored Data

This paper deals with the problem of parameters estimation of the Exponential-Geometric (EG) distribution based on progressive type-II censored data. It turns out that the maximum likelihood estimators for the distribution parameters have no closed forms, therefore the EM algorithm are alternatively used. The asymptotic variance of the MLEs of the targeted parameters under progressive type-II censoring is computed along with the asymptotic confidence intervals. Finally, a simple numerical example is given to illustrate the obtained results.

scholarly journals The extended odd family of probability distributions with practice to a submodel

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3855-3867 ◽  
Author(s):  
Hassan Bakouch ◽  
Christophe Chesneau ◽  
Muhammad Khan
Keyword(s):  
Heavy Tails ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Likelihood Method ◽  
Tuning Parameter ◽  
Data Sets ◽  
New Family ◽  
Rate Functions ◽  
Special Case ◽  
Family Of Distributions

In this paper, we introduce a new family of distributions extending the odd family of distributions. A new tuning parameter is introduced, with some connections to the well-known transmuted transformation. Some mathematical results are obtained, including moments, generating function and order statistics. Then, we study a special case dealing with the standard loglogistic distribution and the modifiedWeibull distribution. Its main features are to have densities with flexible shapes where skewness, kurtosis, heavy tails and modality can be observed, and increasing-decreasing-increasing, unimodal and bathtub shaped hazard rate functions. Estimation of the related parameters is investigated by the maximum likelihood method. We illustrate the usefulness of our extended odd family of distributions with applications to two practical data sets.

The Maple Syrup Problem Revisited: MCMC with Gibbs Sampling

2019 ◽  
pp. 247-266
Author(s):  
Therese M. Donovan ◽  
Ruth M. Mickey
Keyword(s):  
Monte Carlo ◽  
Gibbs Sampling ◽  
Posterior Distribution ◽  
Unknown Parameter ◽  
The Other ◽  
Sampling Step ◽  
Maple Syrup ◽  
Two Parameters ◽  
Special Case ◽  
Joint Posterior Distribution

This chapter introduces Markov Chain Monte Carlo (MCMC) with Gibbs sampling, revisiting the “Maple Syrup Problem” of Chapter 12, where the goal was to estimate the two parameters of a normal distribution, μ‎ and σ‎. Chapter 12 used the normal-normal conjugate to derive the posterior distribution for the unknown parameter μ‎; the parameter σ‎ was assumed to be known. This chapter uses MCMC with Gibbs sampling to estimate the joint posterior distribution of both μ‎ and σ‎. Gibbs sampling is a special case of the Metropolis–Hastings algorithm. The chapter describes MCMC with Gibbs sampling step by step, which requires (1) computing the posterior distribution of a given parameter, conditional on the value of the other parameter, and (2) drawing a sample from the posterior distribution. In this chapter, Gibbs sampling makes use of the conjugate solutions to decompose the joint posterior distribution into full conditional distributions for each parameter.

scholarly journals Efficient Parameters Estimation Methods for Radar Moving Targets Without Searching

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 41351-41361
Author(s):  
Xuepan Zhang ◽  
Chen Yang ◽  
Qingqing Lin ◽  
Xuejing Zhang
Keyword(s):  
Parameters Estimation ◽  
Estimation Methods ◽  
Moving Targets
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