The Truncated Lomax-exponential distribution and its fitting to financial data

Nowadays, analyzing the losses data of the insurance and asset portfolios has special importance in risk analysis and economic problems. Therefore, having suitable distributions that are able to fit such data, is important. In this paper, a new distribution with decreasing failure rate function is introduced. Then, some important and applicable statistical indices in insurance and economics like the moments and moment generating function, value at risk, tail value at risk, tail variance, and Shannon and R\'enyi entropies are obtained. One of the advantages of this distribution is that it has fewer parameters compared to other distributions that have been introduced so far. Finally, this distribution is utilized as a proper distribution to fit on a real data set.

Keywords:

exponential distribution , Value-at-Risk , Tail Value-at-Risk , Tail variance , Mean residual life