scholarly journals On Estimation of Three-Component Mixture of Distributions via Bayesian and Classical Approaches

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Muhammad Tahir ◽  
Ibrahim M. Almanjahie ◽  
Muhammad Abid ◽  
Ishfaq Ahmad
Keyword(s):  
Real Life ◽  
Mixture Distribution ◽  
Type I ◽  
Component Mixture ◽  
Ml Estimation ◽  
Noninformative Priors ◽  
Data Application ◽  
Real Life Data ◽  
Detailed Simulation ◽  
Raphson Method

In this study, we model a heterogeneous population assuming the three-component mixture of the Pareto distributions assuming type I censored data. In particular, we study some statistical properties (such as various entropies, different inequality indices, and order statistics) of the three-component mixture distribution. The ML estimation and the Bayesian estimation of the mixture parameters have been performed in this study. For the ML estimation, we used the Newton Raphson method. To derive the posterior distributions, different noninformative priors are assumed to derive the Bayes estimators. Furthermore, we also discussed the Bayesian predictive intervals. We presented a detailed simulation study to compare the ML estimates and Bayes estimates. Moreover, we evaluated the performance of different estimates assuming various sample sizes, mixing weights and test termination times (a fixed point of time after which all other tests are dismissed). The real-life data application is also a part of this study.

scholarly journals Statistical Analysis of the Mixture of Inverted Exponential Distribution Under Bayesian Approach

2019 ◽  
pp. 1-16
Author(s):  
Tabasam Sultana ◽  
Muhammad Aslam ◽  
Javid Shabbir
Keyword(s):  
Prior Information ◽  
Graphical Representation ◽  
Simulation Analysis ◽  
Real Life ◽  
Type I ◽  
Bayes Estimators ◽  
Exponential Distributions ◽  
Component Mixture ◽  
Real Life Data ◽  
Censored Sampling

This paper is about studying a 3-component mixture of the Inverted Exponential distributions under Bayesian view point. The type-I right censored sampling scheme is considered because of its extensive use in reliability theory and survival analysis. The expressions for the Bayes estimators and their posterior risks are derived under dierent loss scenarios. In case, no or little prior information is available, elicitation of hyper parameters is given. In order to study numerically, the execution of the Bayes estimators under dierent loss functions, their statistical properties have been simulated for dierent sample sizes and test termination times. A real life data example is given to illustrate the study. Graphical representation of the simulation analysis results is also given to study the properties of the Bayes estimators.

scholarly journals Estimation of Regression Parameters from Noise Multiplied Data

2013 ◽  
Vol 4 (2) ◽  
Author(s):  
Yan-Xia Lin ◽  
Phillip Wise
Keyword(s):  
Regression Analysis ◽  
Regression Model ◽  
Real Life ◽  
Simulation Studies ◽  
Independent Variables ◽  
Multiplicative Noises ◽  
Life Data ◽  
Regression Parameters ◽  
Data Application ◽  
Real Life Data

This paper considers the scenario that all data entries in a confidentialised unit record file were masked by multiplicative noises, regardless of whether unit records are sensitive or not and regardless of whether the masked variables are dependent or independent variables in the underlying regression analysis. A technique is introduced in this paper to show how to estimate parameters in a regression model, which is originally fitted by unmasked data, based on masked data. Several simulation studies and a real-life data application are presented.

scholarly journals Extended Gumbel Type-2 Distribution: Properties and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
A. A. Ogunde ◽  
S. T. Fayose ◽  
B. Ajayi ◽  
D. O. Omosigho
Keyword(s):  
Information Matrix ◽  
Real Life ◽  
Moment Generating Function ◽  
Type I ◽  
Survival Times ◽  
Life Data ◽  
Distributional Properties ◽  
Real Life Data ◽  
Cancer Remission

In this paper, we proposed a new four-parameter Extended Gumbel type-2 distribution which can further be split into the Lehman type I and type II Gumbel type-2 distribution by using a generalized exponentiated G distribution. The distributional properties of the proposed distribution have been studied. We derive the p th moment; thus, we generalize some results in the literature. Expressions for the density, moment-generating function, and r th moment of the order statistics are also obtained. We discuss estimation of the parameters by maximum likelihood and provide the information matrix of the developed distribution. Two life data, which consist of data on cancer remission times and survival times of pigs, were used to show the applicability of the Extended Gumbel type-2 distribution in modelling real life data, and we found out that the new model is more flexible than its submodels.

PSY24 PATIENT TREATMENTS PREFERENCES: HOW TO IDENTIFY PATIENT PROFILES DIRECTLY FROM ONLINE REAL-LIFE DATA? APPLICATION TO LUPUS

2020 ◽  
Vol 23 ◽  
pp. S375
Author(s):  
D. Testa ◽  
L. Radoszycki ◽  
V. Morisseau ◽  
C. Fidyk ◽  
L. Chiche
Keyword(s):  
Real Life ◽  
Life Data ◽  
Data Application ◽  
Real Life Data ◽  
Patient Profiles

scholarly journals Analysis of novel fractional COVID-19 model with real-life data application

2021 ◽  
Vol 23 ◽  
pp. 103968 ◽  
Author(s):  
Mustafa Inc ◽  
Bahar Acay ◽  
Hailay Weldegiorgis Berhe ◽  
Abdullahi Yusuf ◽  
Amir Khan ◽  
...  
Keyword(s):  
Real Life ◽  
Life Data ◽  
Data Application ◽  
Real Life Data

scholarly journals Count Data Time Series Modelling in Julia—The CountTimeSeries.jl Package and Applications

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 666
Author(s):  
Manuel Stapper
Keyword(s):  
Time Series ◽  
Real Life ◽  
Theoretical Background ◽  
Information Criteria ◽  
Finite Sample ◽  
Ml Estimation ◽  
Real Life Data ◽  
Time Series Modelling ◽  
Finite Sample Properties ◽  
Count Data Time Series

A new software package for the Julia language, CountTimeSeries.jl, is under review, which provides likelihood based methods for integer-valued time series. The package’s functionalities are showcased in a simulation study on finite sample properties of Maximum Likelihood (ML) estimation and three real-life data applications. First, the number of newly infected COVID-19 patients is predicted. Then, previous findings on the need for overdispersion and zero inflation are reviewed in an application on animal submissions in New Zealand. Further, information criteria are used for model selection to investigate patterns in corporate insolvencies in Rhineland-Palatinate. Theoretical background and implementation details are described, and complete code for all applications is provided online. The CountTimeSeries package is available at the general Julia package registry.

scholarly journals Estimation Methods for a Flexible INAR(1) COM-Poisson Time Series Model

2018 ◽  
Vol 14 (1) ◽  
pp. 57-82 ◽  
Author(s):  
Y. Sunecher ◽  
N. Mamode Khan ◽  
V. Jowaheer
Keyword(s):  
Time Series ◽  
Real Life ◽  
Estimation Methods ◽  
Unknown Parameters ◽  
Simulation Experiments ◽  
Time Series Of Counts ◽  
First Order ◽  
Life Data ◽  
Data Application ◽  
Real Life Data

Abstract Time series of counts occur in many real-life situations where they exhibit various forms of dispersion. To facilitate the modeling of such time series, this paper introduces a flexible first-order integer-valued non-stationary autoregressive (INAR(1)) process where the innovation terms follow a Conway-Maxwell Poisson distribution (COM-Poisson). To estimate the unknown parameters in this model, different estimation approaches based on likelihood and quasi-likelihood formulations are considered. From simulation experiments and a real-life data application, the Generalized Quasi-Likelihood (GQL) approach yields estimates with lower bias than the other estimation approaches.

scholarly journals Properties and Applications of the Modified Kies–Lomax Distribution with Estimation Methods

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Abdelaziz Alsubie
Keyword(s):  
Real Life ◽  
Estimation Method ◽  
Estimation Methods ◽  
Lomax Distribution ◽  
Estimation Algorithms ◽  
Real Life Data ◽  
Detailed Simulation ◽  
Relative Errors ◽  
Rival Models ◽  
Mean Square Errors

The present study introduces a new three-parameter model called the modified Kies–Lomax (MKL) distribution to extend the Lomax distribution and increase its flexibility in modeling real-life data. The MKL distribution, due to its flexibility, provides left-skewed, symmetrical, right-skewed, and reversed-J shaped densities and increasing, unimodal, decreasing, and bathtub hazard rate shapes. The MKF density can be expressed as a linear mixture of Lomax densities. Some basic mathematical properties of the MKF model are derived. Its parameters are estimated via six estimation algorithms. We explore their performances using detailed simulation results, and the partial and overall ranks are provided for the measures of absolute biases, mean square errors, and mean relative errors to determine the best estimation method. The results show that the maximum product of spacings and maximum likelihood approaches are recommended to estimate the MKL parameters. Finally, the flexibility of the MKL distribution is checked using two real datasets, showing that it can provide close fit to both datasets as compared with other competing Lomax models. The three-parameter MKL model outperforms some four-parameter and five-parameter rival models.

scholarly journals A Novel Computational Tool for Mining Real-Life Data: Application in the Metastatic Colorectal Cancer Care Setting

PLoS ONE ◽  
2016 ◽  
Vol 11 (5) ◽  
pp. e0154689
Author(s):  
Nava Siegelmann-Danieli ◽  
Ariel Farkash ◽  
Itzhak Katzir ◽  
Janet Vesterman Landes ◽  
Hadas Rotem Rabinovich ◽  
...  
Keyword(s):  
Colorectal Cancer ◽  
Metastatic Colorectal Cancer ◽  
Cancer Care ◽  
Care Setting ◽  
Real Life ◽  
Computational Tool ◽  
Life Data ◽  
Data Application ◽  
Real Life Data

scholarly journals EM Estimation for Zero- and k-Inflated Poisson Regression Model

Computation ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 94
Author(s):  
Monika Arora ◽  
N. Rao Chaganty
Keyword(s):  
Regression Model ◽  
Expectation Maximization ◽  
Real Life ◽  
Mixture Distribution ◽  
Distribution Model ◽  
Parameter Estimates ◽  
Stochastic Representation ◽  
Fundamental Properties ◽  
Real Life Data ◽  
Information Matrices

Count data with excessive zeros are ubiquitous in healthcare, medical, and scientific studies. There are numerous articles that show how to fit Poisson and other models which account for the excessive zeros. However, in many situations, besides zero, the frequency of another count k tends to be higher in the data. The zero- and k-inflated Poisson distribution model (ZkIP) is appropriate in such situations The ZkIP distribution essentially is a mixture distribution of Poisson and degenerate distributions at points zero and k. In this article, we study the fundamental properties of this mixture distribution. Using stochastic representation, we provide details for obtaining parameter estimates of the ZkIP regression model using the Expectation–Maximization (EM) algorithm for a given data. We derive the standard errors of the EM estimates by computing the complete, missing, and observed data information matrices. We present the analysis of two real-life data using the methods outlined in the paper.

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