A novel loss model: peaks over random threshold and the mean of order- <i>P</i> analysis under US indemnity loss

In this paper, a new trigonometric family is proposed for actuarial risk analysis. The Secant Dagum loss distribution is considered a special case. Simulations are carried out to ascertain the behavior of the estimators. The parameters are obtained using the maximum likelihood estimation technique. The usefulness of the new loss distribution is demonstrated with the Norwegian fire loss and US indemnity loss datasets. The analysis of value-at-risk, tail mean-variance, tail variance, peaks over a random threshold value-at-risk and the mean of order-P (MOOP(P)) can assist in risk analysis and in identifying and describing significant events or outliers within the US indemnity loss dataset. In this study, Peaks Over a Random Threshold value-at-risk estimators are developed and adapted specifically for risk analysis using the US indemnity loss dataset. The focus is on determining the optimal order of P based on the true mean value, enhancing the characterization of critical events in the dataset.