COMPUTATION OF MAXIMUM LIKELIHOOD ESTIMATES OF GRAVITY MODEL PARAMETERS*

1994 ◽  
Vol 34 (2) ◽  
pp. 199-216 ◽  
Author(s):  
Seongsoon Yun ◽  
Ashish Sen
Keyword(s):  
Maximum Likelihood ◽  
Gravity Model ◽  
Maximum Likelihood Estimates ◽  
Model Parameters

scholarly journals A Family of Loss Distributions with an Application to the Vehicle Insurance Loss Data

2019 ◽  
pp. 731-744 ◽  
Author(s):  
Zubair Ahmad Ahmad ◽  
Eisa Mahmoudi Mahmoudi ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Financial Risk ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Set ◽  
Loss Model ◽  
New Class ◽  
Proposed Model ◽  
Loss Distributions ◽  
Loss Data

Actuaries are often in search of nding an adequate loss model in the scenario of actuarial and financial risk management problems. In this work, we propose a new approach to obtain a new class of loss distributions. A special sub-model of the proposed family, called the Weibull-loss model isconsidered in detail. Some mathematical properties are derived and maximum likelihood estimates of the model parameters are obtained. Certain characterizations of the proposed family are also provided. A simulation study is done to evaluate the performance of the maximum likelihood estimators. Finally, an application of the proposed model to the vehicle insurance loss data set is presented.

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

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 Generalized Weighted Rama Distribution: Properties and Application to Model Lifetime Data

2021 ◽  
pp. 9-37
Author(s):  
Samuel U. Enogwe ◽  
Chisimkwuo John ◽  
Happiness O. Obiora-Ilouno ◽  
Chrisogonus K. Onyekwere
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Bathtub Shape ◽  
Asymptotic Confidence Intervals

In this paper, we propose a new lifetime distribution called the generalized weighted Rama (GWR) distribution, which extends the two-parameter Rama distribution and has the Rama distribution as a special case. The GWR distribution has the ability to model data sets that have positive skewness and upside-down bathtub shape hazard rate. Expressions for mathematical and reliability properties of the GWR distribution have been derived. Estimation of parameters was achieved using the method of maximum likelihood estimation and a simulation was performed to verify the stability of the maximum likelihood estimates of the model parameters. The asymptotic confidence intervals of the parameters of the proposed distribution are obtained. The applicability of the GWR distribution was illustrated with a real data set and the results obtained show that the GWR distribution is a better candidate for the data than the other competing distributions being investigated.

scholarly journals Parameter Estimation of a Multistate Model for an Aging Piece of Equipment under Condition-Based Maintenance

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Qihong Duan ◽  
Xiang Chen ◽  
Dengfu Zhao ◽  
Zheng Zhao
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Model Calculation ◽  
Expectation Maximization ◽  
Expectation Maximization Algorithm ◽  
Condition Based Maintenance ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Simulation Studies ◽  
Multistate Model

We study a multistate model for an aging piece of equipment under condition-based maintenance and apply an expectation maximization algorithm to obtain maximum likelihood estimates of the model parameters. Because of the monitoring discontinuity, we cannot observe any state's duration. The observation consists of the equipment's state at an inspection or right after a repair. Based on a proper construction of stochastic processes involved in the model, calculation of some probabilities and expectations becomes tractable. Using these probabilities and expectations, we can apply an expectation maximization algorithm to estimate the parameters in the model. We carry out simulation studies to test the accuracy and the efficiency of the algorithm.

A Selected Review of Risk Models: One Hit, Multihit, Multistage, Probit, Weibull, and Pharmacokinetic

1985 ◽  
Vol 4 (4) ◽  
pp. 271-278 ◽  
Author(s):  
B. Hanes ◽  
T. Wedel
Keyword(s):  
Maximum Likelihood ◽  
Risk Model ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Confidence Limits ◽  
Risk Models ◽  
Sufficient Detail ◽  
The One

This paper provides some of the underlying mathematical derivations for the one-hit, multihit, multistage, Weibull, and pharmacokinetic risk models. Our purposes are to remove for the nonmathematician some of the mystery as to the derivation of the formulas for each particular risk model and to discuss some of the assumptions contained in the risk models. Confidence limits and maximum likelihood estimates of the model parameters are not discussed, since they are not pertinent to our objectives. Rai and Van Ryzin(1) have outlined these procedures in sufficient detail.

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