scholarly journals An algorithm for the assessment of several small rates

2012 ◽  
Vol 53 ◽  
Author(s):  
Leonidas Sakalauskas ◽  
Ingrida Vaičiulytė
Keyword(s):  
Maximum Likelihood ◽  
Bayesian Approach ◽  
Maximum Likelihood Method ◽  
Rare Events ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Empirical Bayesian ◽  
Empirical Bayesian Approach

The present paper describes the empirical Bayesian approach applied in the estimation of several small rates. Modeling by empirical Bayesian approach the probabilities of several rare events, it is assumed that the frequencies of events follow to Poisson’s law with different parameters, which are correlated Gaussian random values. The unknown parameters are estimated by the maximum likelihood method computing the integrals appeared here by Hermite–Gauss quadratures. The equations derived that are satisfied by maximum likelihood estimates of model parameters.

scholarly journals The four-parameter Fréchet distribution: Properties and applications

2020 ◽  
pp. 249-264
Author(s):  
Mohamed Hamed ◽  
Fahad Aldossary ◽  
Ahmed Z. Afify
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Model Parameters ◽  
Fréchet Distribution ◽  
Mathematical Properties ◽  
Modeling Data ◽  
Frechet Distribution

In this article, we propose a new four-parameter Fréchet distribution called the odd Lomax Fréchet distribution. The new model can be expressed as a linear mixture of Fréchet densities. We provide some of its mathematical properties. The estimation of the model parameters is performed by the maximum likelihood method. We illustrate the good performance of the maximum likelihood estimates via a detailed numerical simulation study. The importance and usefulness of the proposed distribution for modeling data are illustrated using two real data applications.

scholarly journals Robust parametric estimates of inhomogeneous experimental data

2020 ◽  
pp. 55-62
Author(s):  
V.A. Simakhin ◽  
◽  
L.G. Shamanaeva ◽  
A.E. Avdyushina ◽  
◽  
...  
Keyword(s):  
Experimental Data ◽  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Robust Estimates

In the present work, a weighed maximum likelihood method (WMLM) is proposed to obtain robust estimates for processing experimental data containing outliers. The method allows robust asymptotic unbiased and effective estimates to be obtained in the presence of not only external, but also internal asymmetric and symmetric outliers. Algorithms for obtaining robust WMLM estimates are considered at the parametric level of aprioristic uncertainty. It is demonstrated that these estimates converge to maximum likelihood estimates of an inhomogeneous sample for each distribution from the Tukey supermodel.

scholarly journals On Modified Burr XII-Inverse Weibull Distribution: Development, Properties, Characterizations and Applications

2020 ◽  
pp. 721-735
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Haitham M. Yousof ◽  
Azeem Ali ◽  
Munir Ahmad
Keyword(s):  
Maximum Likelihood ◽  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Quarterly Earnings ◽  
Inverse Weibull Distribution

A flexible lifetime distribution with increasing, decreasing, inverted bathtub and modified bathtub hazard rate called Modified Burr XII-Inverse Weibull (MBXII-IW) is introduced and studied. The density function of MBXII-IW is exponential, left-skewed, right-skewed and symmetrical shaped.  Descriptive measures on the basis of quantiles, moments, order statistics and reliability measures are theoretically established. The MBXII-IW distribution is characterized via different techniques. Parameters of MBXII-IW distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of MBXII-IW distribution is demonstrated by its application to real data sets: serum-reversal times and quarterly earnings.

scholarly journals A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 440 ◽  
Author(s):  
Abdulhakim A. Al-babtain ◽  
I. Elbatal ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Simple Type ◽  
Data Sets ◽  
New Model ◽  
Clayton Copula ◽  
Mathematical Properties

In this article, we introduced a new extension of the binomial-exponential 2 distribution. We discussed some of its structural mathematical properties. A simple type Copula-based construction is also presented to construct the bivariate- and multivariate-type distributions. We estimated the model parameters via the maximum likelihood method. Finally, we illustrated the importance of the new model by the study of two real data applications to show the flexibility and potentiality of the new model in modeling skewed and symmetric data sets.

scholarly journals Asymptotic properties of M-estimator for GARCH(1, 1) model parameters

2020 ◽  
pp. 69-78
Author(s):  
Uladzimir S. Tserakh
Keyword(s):  
Maximum Likelihood ◽  
Heavy Tails ◽  
Maximum Likelihood Method ◽  
Asymptotic Properties ◽  
Likelihood Method ◽  
Model Parameters ◽  
Economic Time Series ◽  
Volatility Clustering ◽  
Asymptotically Normal ◽  
M Estimator

GARCH(1,  1) model is used for analysis and forecasting of financial and economic time series. In the classical version, the maximum likelihood method is used to estimate the model parameters. However, this method is not convenient for analysis of models with residuals distribution different from normal. In this paper, we consider M-estimator for the GARCH(1,  1) model parameters, which is a generalization of the maximum likelihood method. An algorithm for constructing an M-estimator is described and its asymptotic properties are studied. A set of conditions is formulated under which the estimator is strictly consistent and has an asymptotically normal distribution. This method allows to analyze models with different residuals distributions; in particular, models with stable and tempered stable distributions that allow to take into account the features of real financial data: volatility clustering, heavy tails, asymmetry.

scholarly journals Lehmann Type II Frechet Poisson Distribution: Properties, Inference and Applications as a Life Time Distribution

2021 ◽  
Vol 10 (3) ◽  
pp. 8
Author(s):  
Adebisi Ade Ogunde ◽  
Gbenga Adelekan Olalude ◽  
Oyebimpe Emmanuel Adeniji ◽  
Kayode Balogun
Keyword(s):  
Maximum Likelihood ◽  
Poisson Distribution ◽  
Maximum Likelihood Method ◽  
Life Time ◽  
Real Data ◽  
Likelihood Method ◽  
Strength Parameter ◽  
Model Parameters ◽  
Type Ii ◽  
Time Data

A new generalization of the Frechet distribution called Lehmann Type II Frechet Poisson distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary moments, incomplete moments, generating functions, order statistics, Renyi entropy, stochastic ordering, Bonferroni and Lorenz curve, mean and median deviation, stress-strength parameter are investigated. The maximum likelihood method is used to estimate the model parameters. We examine the performance of the maximum likelihood method by means of a numerical simulation study. The new distribution is applied for modeling three real data sets to illustrate empirically its flexibility and tractability in modeling life time data.

scholarly journals Multivariate Skew-Power-Normal Distributions: Properties and Associated Inference

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1509
Author(s):  
Guillermo Martínez-Flórez ◽  
Artur J. Lemonte ◽  
Hugo S. Salinas
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Multivariate Distributions ◽  
Likelihood Approach ◽  
Information Matrices ◽  
Univariate Distribution

The univariate power-normal distribution is quite useful for modeling many types of real data. On the other hand, multivariate extensions of this univariate distribution are not common in the statistic literature, mainly skewed multivariate extensions that can be bimodal, for example. In this paper, based on the univariate power-normal distribution, we extend the univariate power-normal distribution to the multivariate setup. Structural properties of the new multivariate distributions are established. We consider the maximum likelihood method to estimate the unknown parameters, and the observed and expected Fisher information matrices are also derived. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. An empirical application of the proposed multivariate distribution to real data is provided for illustrative purposes.

scholarly journals A New Family of Continuous Probability Distributions

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 194
Author(s):  
M. El-Morshedy ◽  
Fahad Sameer Alshammari ◽  
Yasser S. Hamed ◽  
Mohammed S. Eliwa ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Real Life ◽  
Likelihood Method ◽  
Model Parameters ◽  
Finite Sample ◽  
Graphical Simulation ◽  
New Family ◽  
The One

In this paper, a new parametric compound G family of continuous probability distributions called the Poisson generalized exponential G (PGEG) family is derived and studied. Relevant mathematical properties are derived. Some new bivariate G families using the theorems of “Farlie-Gumbel-Morgenstern copula”, “the modified Farlie-Gumbel-Morgenstern copula”, “the Clayton copula”, and “the Renyi’s entropy copula” are presented. Many special members are derived, and a special attention is devoted to the exponential and the one parameter Pareto type II model. The maximum likelihood method is used to estimate the model parameters. A graphical simulation is performed to assess the finite sample behavior of the estimators of the maximum likelihood method. Two real-life data applications are proposed to illustrate the importance of the new family.

Sign in / Sign up

Export Citation Format

Share Document