Analysis of skewed data by using compound Poisson exponential distribution with applications to insurance claims

2021 ◽  
pp. 1-29
Author(s):  
Mohammed A. Meraou ◽  
Noriah M. Al-Kandari ◽  
Mohammad Z. Raqab ◽  
Debasis Kundu
Keyword(s):  
Exponential Distribution ◽  
Skewed Data ◽  
Insurance Claims ◽  
Compound Poisson

scholarly journals A Note on a Generalized Gerber–Shiu Discounted Penalty Function for a Compound Poisson Risk Model

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 891 ◽  
Author(s):  
Jiechang Ruan ◽  
Wenguang Yu ◽  
Ke Song ◽  
Yihan Sun ◽  
Yujuan Huang ◽  
...  
Keyword(s):  
Laplace Transform ◽  
Exponential Distribution ◽  
Penalty Function ◽  
Risk Model ◽  
Recursive Method ◽  
Ruin Time ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Discounted Penalty Function ◽  
Poisson Risk Model

In this paper, we propose a new generalized Gerber–Shiu discounted penalty function for a compound Poisson risk model, which can be used to study the moments of the ruin time. First, by taking derivatives with respect to the original Gerber–Shiu discounted penalty function, we construct a relation between the original Gerber–Shiu discounted penalty function and our new generalized Gerber–Shiu discounted penalty function. Next, we use Laplace transform to derive a defective renewal equation for the generalized Gerber–Shiu discounted penalty function, and give a recursive method for solving the equation. Finally, when the claim amounts obey the exponential distribution, we give some explicit expressions for the generalized Gerber–Shiu discounted penalty function. Numerical illustrations are also given to study the effect of the parameters on the generalized Gerber–Shiu discounted penalty function.

A generalisation of the exponential distribution and its applications on modelling skewed data

2018 ◽  
Vol 2 (1) ◽  
pp. 68-79
Author(s):  
Muhammad Zubair ◽  
Ayman Alzaatreh ◽  
M. H. Tahir ◽  
Muhammad Mansoor ◽  
Manat Mustafa
Keyword(s):  
Exponential Distribution ◽  
Skewed Data

The Approximation of Sum of Independent Distributions by the Erlang Distribution Function

2002 ◽  
Vol 7 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Antanas Karoblis
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Queueing Theory ◽  
Erlang Distribution ◽  
Estimation Of Error

The exponential distribution and the Erlang distribution function are been used in numerous areas of mathematics, and specifically in the queueing theory. Such and similar applications emphasize the importance of estimation of error of approximation by the Erlang distribution function. The article gives an analysis and technique of error’s estimation of an accuracy of such approximation, especially in some specific cases.

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

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