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In probability theory, a random variable (vector) is divided into discrete, absolutely continuous, singular continuous, and a mixture of them. Absolutely discrete and continuous random variables (vectors) have been extensively studied in various probability and statistics books. However, less attention has been paid to the issue of singular continuous distributions and mixture distributions, part of which is singular continuous. In this article, an example of ‎singular‎ random vectors is given. Also, examples of mixture random vectors are presented whose distribution function is a convex linear combination of discrete, absolutely ‎continuous,‎ and continuous distribution functions.

 

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Risk means a situation in which there is a possibility of deviation from a predicted result. Insurance is one of the methods of risk exposure that leads to the transfer of all or part of the risk from the insured to the insurer. Insurance policies are usually classified into two types: personal and non-life (non-life) insurance. According to this classification, any insurance policy that deals with the health of the insured person or persons is a personal insurance policy, otherwise it will be a nonlife insurance policy. Many insurances in the insurance industry are classified as non-life insurances. Fire, automobile, engineering, shipping, oil and energy insurances are examples of these insurances. Explanation and calculation of three issues in risk models are very important: the ruin probability, the time of ruin and the amount of ruin. In this article, the main and well-known results that have been obtained so far in the field of non-life insurance; Emphasizing the possibility of ruin, it is given along with various examples.