scholarly journals A Bayesian Inference Approach for Bivariate Weibull Distributions Derived from Roy and Morgenstern Methods

2021 ◽  
Vol 9 (3) ◽  
pp. 529-554
Author(s):  
Ricardo Puziol de Oliveira ◽  
Marcos Vinicius de Oliveira Peres ◽  
Milene Regina dos Santos ◽  
Edson Zangiacomi Martinez ◽  
Jorge Aberto Achcar
Keyword(s):  
Survival Function ◽  
Factorial Moment ◽  
Simulated Data ◽  
Real Data ◽  
Rate Function ◽  
Strength Parameter ◽  
Numerical Application ◽  
Lifetime Distributions ◽  
Proposed Model ◽  
Joint Survival Function

Bivariate lifetime distributions are of great importance in studies related to interdependent components, especially in engineering applications. In this paper, we introduce two bivariate lifetime assuming three- parameter Weibull marginal distributions. Some characteristics of the proposed distributions as the joint survival function, hazard rate function, cross factorial moment and stress-strength parameter are also derived. The inferences for the parameters or even functions of the parameters of the models are obtained under a Bayesian approach. An extensive numerical application using simulated data is carried out to evaluate the accuracy of the obtained estimators to illustrate the usefulness of the proposed methodology. To illustrate the usefulness of the proposed model, we also include an example with real data from which it is possible to see that the proposed model leads to good fits to the data.

A fuzzy rumor spreading model based on transmission capacity

2018 ◽  
Vol 29 (02) ◽  
pp. 1850012 ◽  
Author(s):  
Yi Zhang ◽  
Jiuping Xu ◽  
Yue Wu
Keyword(s):  
Simulated Data ◽  
Real Data ◽  
Transmission Capacity ◽  
Model Assessment ◽  
Rumor Spreading ◽  
Factors Affecting ◽  
Fuzzy Variables ◽  
Spreading Model ◽  
Proposed Model ◽  
Special Cases

This paper proposes a rumor spreading model that considers three main factors: the event importance, event ambiguity, and the publics critical sense, each of which are defined by decision makers using linguistic descriptions and then transformed into triangular fuzzy numbers. To calculate the resultant force of these three factors, the transmission capacity and a new parameter category with fuzzy variables are determined. A rumor spreading model is then proposed which has fuzzy parameters rather than the fixed parameters in traditional models. As the proposed model considers the comprehensive factors affecting rumors from three aspects rather than examining special factors from a particular aspect. The proposed rumor spreading model is tested using different parameters for several different conditions on BA networks and three special cases are simulated. The simulation results for all three cases suggested that events of low importance, those that are only clarifying facts, and those that are strongly critical do not result in rumors. Therefore, the model assessment results were proven to be in agreement with reality. Parameters for the model were then determined and applied to an analysis of the 7.23 Yong–Wen line major transportation accident (YWMTA). When the simulated data were compared with the real data from this accident, the results demonstrated that the interval for the rumor spreading key point in the model was accurate, and that the key point for the YWMTA rumor spread fell into the range estimated by the model.

scholarly journals The Inverse Sushila Distribution: Properties and Application

2020 ◽  
pp. 28-39
Author(s):  
A. A. Adetunji ◽  
J. A. Ademuyiwa ◽  
O. A. Adejumo
Keyword(s):  
Hazard Rate ◽  
Survival Function ◽  
Likelihood Estimation ◽  
Stochastic Ordering ◽  
Rate Function ◽  
Lifetime Data ◽  
Hazard Rate Function ◽  
Cumulative Hazard ◽  
Fundamental Properties ◽  
Proposed Model

In this paper, a new lifetime distribution called the Inverse Sushila Distribution (ISD) is proposed. Its fundamental properties like the density function, distribution function, hazard rate function, survival function, cumulative hazard rate function, order statistics, moments, moments generating function, maximum likelihood estimation, quantiles function, Rényi entropy and stochastic ordering are obtained. The distribution offers more flexibility in modelling upside-down bathtub lifetime data. The proposed model is applied to a lifetime data and its performance is compared with some other related distributions.

scholarly journals The Half-Logistic Lomax Distribution for Lifetime Modeling

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Masood Anwar ◽  
Jawaria Zahoor
Keyword(s):  
Maximum Likelihood ◽  
Residual Life ◽  
Information Matrix ◽  
Simulated Data ◽  
Quantile Function ◽  
Rate Function ◽  
Mean Residual Life ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Proposed Model

We introduce a new two-parameter lifetime distribution called the half-logistic Lomax (HLL) distribution. The proposed distribution is obtained by compounding half-logistic and Lomax distributions. We derive some mathematical properties of the proposed distribution such as the survival and hazard rate function, quantile function, mode, median, moments and moment generating functions, mean deviations from mean and median, mean residual life function, order statistics, and entropies. The estimation of parameters is performed by maximum likelihood and the formulas for the elements of the Fisher information matrix are provided. A simulation study is run to assess the performance of maximum-likelihood estimators (MLEs). The flexibility and potentiality of the proposed model are illustrated by means of real and simulated data sets.

scholarly journals Using Cauchy Distribution To Estimate Survival Function

2021 ◽  
Vol 12 (4) ◽  
pp. 1014-1023
Author(s):  
Hind Jawad Kadhim Al Bderi
Keyword(s):  
Survival Function ◽  
Real Data ◽  
Cauchy Distribution ◽  
Ordinary Least Squares ◽  
Rate Function ◽  
Cumulative Distribution ◽  
Distribution Model ◽  
Point Estimators ◽  
Percentage Measure ◽  
Two Parameters

This paper intends to estimate the unlabeled two parameters for Cauchy distribution model depend on employing the maximum likelihood estimator method  to obtain the derivation of the point estimators for all unlabeled parameters depending on iterative techniques , as Newton – Raphson method , then to derive “Lindley approximation estimator method and then to derive Ordinary least squares estimator method. Applying all these methods to estimate related probability functions; death density function, cumulative distribution function, survival function and hazard function (rate function)”. “When examining the numerical results for probability survival function by employing mean squares error measure and mean absolute percentage measure, this may lead to work on the best method in modeling a set of real data”

scholarly journals On The Burr XII-Gamma Distribution: Development, Properties, Characterizations and Applications

2021 ◽  
pp. 771-789
Author(s):  
Fiaz Ahmad Bhatti ◽  
Gauss M. Cordeiro ◽  
Mustafa Ç. Korkmaz ◽  
G.G. Hamedani
Keyword(s):  
Random Number Generator ◽  
Likelihood Estimation ◽  
Real Data ◽  
Record Values ◽  
Rate Function ◽  
Data Sets ◽  
Failure Rate Function ◽  
Conditional Moments ◽  
Mathematical Properties ◽  
Proposed Model

We introduce a four-parameter lifetime model with flexible hazard rate called the Burr XII gamma (BXIIG) distribution.  We derive the BXIIG distribution from (i) the T-X family technique and (ii) nexus between the exponential and gamma variables. The failure rate function for the BXIIG distribution is flexible as it can accommodate various shapes such as increasing, decreasing, decreasing-increasing, increasing-decreasing-increasing, bathtub and modified bathtub.  Its density function can take shapes such as exponential, J, reverse-J, left-skewed, right-skewed and symmetrical. To illustrate the importance of the BXIIG distribution, we establish various mathematical properties such as random number generator, ordinary moments, generating function, conditional moments, density functions of record values, reliability measures and characterizations.  We address the maximum likelihood estimation for the parameters. We estimate the adequacy of the estimators via a simulation study. We consider applications to two real data sets to prove empirically the potentiality of the proposed model.

scholarly journals On The Transmuted Powered Moment Exponential Distribution

2021 ◽  
pp. 32-46
Author(s):  
Zafar Iqbal ◽  
Muhammad Rashad ◽  
Abdur Razaq ◽  
Muhammad Salman ◽  
Afsheen Javed
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Survival Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Rate Function ◽  
Data Sets ◽  
Inequality Measures ◽  
New Class

We introduce a new class of lifetime models called the transmuted powered moment exponential distribution. More specifically, the transmuted powered moment exponential distribution covers several new distributions. Survival analysis including survival function, hazard rate function and other related measures are computed. Analytical expressions for various mathematical properties of TPMED including rth moment, quantile function, inequality measures, and parameters are estimated by using maximum likelihood estimation and order statistics are also derived. A simulation study of the proposed distribution is performed. It is discovered that the Maximum Likelihood Estimators are consistent since the bias and Mean Square Error approach to zero when the sample size increases. The usefulness of the model associated with this distribution is illustrated by two real data sets and the new model provides a better fit than the models provided in literature.

Inverse Akash distribution and its applications

2021 ◽  
Vol 20 (2) ◽  
pp. 61-72
Author(s):  
E.W. Okereke ◽  
S.N. Gideon ◽  
J. Ohakwe
Keyword(s):  
Survival Function ◽  
Likelihood Estimation ◽  
Stochastic Ordering ◽  
Real Data ◽  
Rate Function ◽  
Entropy Measure ◽  
Parameter Distribution ◽  
Data Sets ◽  
Inverse Exponential Distribution ◽  
Inverse Lindley Distribution

A new one-parameter distribution named inverse Akash distribution, for modelling lifetime data, has been  introduced. Important statistical properties of the proposed distribution such as the density function, hazard rate function, survival function, stochastic ordering,  entropy   measure, stress-strength reliability and the maximum  likelihood estimation of the parameter of the distribution have been discussed. Two real data sets were employed in illustrating the usefulness of the new distribution. Comparatively, the inverse Akash distribution provided better fits to the data than each of the inverse exponential distribution and inverse Lindley distribution.

NONPARAMETRIC ESTIMATION OF THE REVERSED HAZARD RATE FUNCTION FOR UNCENSORED AND CENSORED DATA

2011 ◽  
Vol 18 (05) ◽  
pp. 417-429 ◽  
Author(s):  
CHATHURI L. JAYASINGHE ◽  
PANLOP ZEEPHONGSEKUL
Keyword(s):  
Censored Data ◽  
Hazard Rate ◽  
Real Data ◽  
Reliability Function ◽  
Rate Function ◽  
Nonparametric Estimator ◽  
Selection Methods ◽  
Actuarial Science ◽  
Lifetime Distributions ◽  
Reversed Hazard Rate

Reversed hazard rate (RHR) function is an important reliability function that is applicable to various fields. Applications can be found in portfolio selection problems in finance, analysis of left-censored data, problems in actuarial science and forensic science involving estimation of exact time of occurrence of a particular event, etc. In this paper, we propose a new nonparametric estimator based on binning techniques for this reliability function for an uncensored sample and then provide an extension for RHR estimation under left censorship. The performance of the proposed estimators were then evaluated using simulations and real data from reliability and related disciplines. The results indicate that the proposed estimator does well for common lifetime distributions with the bin-width selection methods considered.

scholarly journals Properties and Inference for a New Class of Generalized Rayleigh Distributions with an Application

2019 ◽  
Vol 17 (1) ◽  
pp. 700-715
Author(s):  
Hayrinisa Demirci Biçer
Keyword(s):  
Survival Function ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Least Square ◽  
Statistical Characteristics ◽  
Data Sets ◽  
Alpha Power ◽  
Inference Problem ◽  
Proposed Model ◽  
Generalized Rayleigh Distribution

Abstract In the present paper, we introduce a new form of generalized Rayleigh distribution called the Alpha Power generalized Rayleigh (APGR) distribution by following the idea of extension of the distribution families with the Alpha Power transformation. The introduced distribution has the more general form than both the Rayleigh and generalized Rayleigh distributions and provides a better fit than the Rayleigh and generalized Rayleigh distributions for more various forms of the data sets. In the paper, we also obtain explicit forms of some important statistical characteristics of the APGR distribution such as hazard function, survival function, mode, moments, characteristic function, Shannon and Rényi entropies, stress-strength probability, Lorenz and Bonferroni curves and order statistics. The statistical inference problem for the APGR distribution is investigated by using the maximum likelihood and least-square methods. The estimation performances of the obtained estimators are compared based on the bias and mean square error criteria by a conducted Monte-Carlo simulation on small, moderate and large sample sizes. Finally, a real data analysis is given to show how the proposed model works in practice.

scholarly journals The Topp-Leone Generalized Inverted Exponential Distribution with Real Data Applications

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1144
Author(s):  
Zakeia A. Al-Saiary ◽  
Rana A. Bakoban
Keyword(s):  
Maximum Likelihood ◽  
Survival Function ◽  
Information Matrix ◽  
Real Data ◽  
Quantile Function ◽  
Rate Function ◽  
Mean Deviation ◽  
Data Sets ◽  
Unknown Parameters ◽  
Illustrative Purpose

In this article, a new three parameters lifetime model called the Topp-Leone Generalized Inverted Exponential (TLGIE) Distribution is introduced. Various properties of the model are derived, including moments, quantile function, survival function, hazard rate function, mean deviation and mode. The method of maximum likelihood is used to estimate the unknown parameters. The properties of the maximum likelihood estimators using Fisher information matrix are studied. Three real data sets are applied for illustrative purpose of this study.

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