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APPROXIMATION OF RANDOM SUMS OF RANDOM VARIABLES IN INSURANCE
Paweł Wlaź 1  
 
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Department of Applied Mathematics, Lublin University of Technology, Nadbystrzycka 38, 20-618 Lublin, Poland
Publication date: 2014-09-09
 
Adv. Sci. Technol. Res. J. 2014; 8(23):88–93
 
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ABSTRACT
The paper deals with approximations of random sums. By random sum we mean a sum of random number of independent and identically distributed random variables. Distribution of this sum is called a compound distribution. The model is especially important in non-life insurance. There are many methods for approximating compound distributions, one of the most popular one is approximation with shifted gamma distribution. In this work we show an alternative way – using kernel density, Fast Fourier Transform and numerical optimization methods – for finding shifted gamma approximations and show results suggesting its superiority over classical method.