On Some Properties of Copula-Based Partial Moments

Partial moments are extensively used in the field of analysis of risks. This paper aims at extending it to the bivariate case based on copula function and study its various properties. The relationship between survival copula and first-order bivariate partial moments are established. We also investigate some applications of copula-based partial moments and conditional partial moments in the context of reliability, income and actuarial studies.

Executive branch federal civil servant mortality by sex and educational level - 1993/2014

ABSTRACT Life tables have been elaborated throughout much of human history. However, the first life table to use actuarial concepts was only constructed in 1815 by Milne for the city of Carlisle in England. Since then, numerous tables have been elaborated for different regions and countries, due to their crucial importance for analyzing various types of problems covering a vast range of possibilities, from actuarial studies to forecasting and evaluating demands in order to define public policies. The most common problem nowadays in an actuarial calculation is choosing a suitable table for a given population. Brazil has few specific tables for the pensions market and has been using imported tables that refer to other countries, with different cultures and different mortality experiences. Using data from the Integrated Human Resource Administration System, this table constructs life tables for Executive branch federal civil servants for the period from 1993 to 2014, disaggregated for sex, age, and educational level (high school and university). The international literature has recognized differences in mortality due to sex, socioeconomic differences, and occupation. The creation of the Complementary Pension Foundation for Federal Public Servants in 2013 requires specific mortality tables for this population to support actuarial studies, healthcare, and personnel policies. A mathematical equation is fitted to the data. This equation can be broken down into infant mortality (not present in the data), mortality from external causes, and mortality from senescence. Recent results acknowledging an upper limit for old age mortality are incorporated into the adjusted probabilities of death. Assuming a binomial distribution for deaths, the deviance was used as a figure of merit to evaluate the goodness of fit of the observed data both to a set of tables used by the insurance/pensions market and to the adjusted tables.

Increasing Hazard Rate of Mixtures for Natural Exponential Families

Hazard rates play an important role in various areas, e.g. reliability theory, survival analysis, biostatistics, queueing theory, and actuarial studies. Mixtures of distributions are also of great preeminence in such areas as most populations of components are indeed heterogeneous. In this study we present a sufficient condition for mixtures of two elements of the same natural exponential family (NEF) to have an increasing hazard rate. We then apply this condition to some classical NEFs having either quadratic or cubic variance functions (VFs) and others as well. Particular attention is paid to the hyperbolic cosine NEF having a quadratic VF, the Ressel NEF having a cubic VF, and the NEF generated by Kummer distributions of type 2. The application of such a sufficient condition is quite intricate and cumbersome, in particular when applied to the latter three NEFs. Various lemmas and propositions are needed to verify this condition for such NEFs. It should be pointed out, however, that our results are mainly applied to a mixture of two populations.

Increasing Hazard Rate of Mixtures for Natural Exponential Families

Hazard rates play an important role in various areas, e.g. reliability theory, survival analysis, biostatistics, queueing theory, and actuarial studies. Mixtures of distributions are also of great preeminence in such areas as most populations of components are indeed heterogeneous. In this study we present a sufficient condition for mixtures of two elements of the same natural exponential family (NEF) to have an increasing hazard rate. We then apply this condition to some classical NEFs having either quadratic or cubic variance functions (VFs) and others as well. Particular attention is paid to the hyperbolic cosine NEF having a quadratic VF, the Ressel NEF having a cubic VF, and the NEF generated by Kummer distributions of type 2. The application of such a sufficient condition is quite intricate and cumbersome, in particular when applied to the latter three NEFs. Various lemmas and propositions are needed to verify this condition for such NEFs. It should be pointed out, however, that our results are mainly applied to a mixture of two populations.

The smoothness criterion as a trend diagnostic

The smoothness criterion is used in the design of symmetric moving average trend filters in time series and in graduation in actuarial studies. This measure of smoothness is used to motivate a diagnostic for determining the order of local polynomial trend.