Afrika Statistika

Infinite variance stable Gegenbaeur Arfisma models

2024-11-26T05:10:16+00:00

This paper develops the theory of the Gegenbauer AutoRegressive Fractionally Integrated Seasonal Moving Average (GARFISMA) process with α-stable innovations. We establish its conditions for causality and invertibility. This is a finite parameter process which exhibits high variability, long memory, cyclical, and seasonality in financial, hydrological data studies, and more. We perform some simulations to illustrate the behavior of our process.

Graduation of term assurance data using frailty approach

2024-11-26T05:18:49+00:00

Frailty models have been used in literature to account for heterogeneity among insureds in-terms of mortality. In this article, we compare the gamma and the non-central gamma as frailty distributions with the exponentiated exponential and exponentiated Weibull as baseline hazards. We adopt a fully Bayesian approach to calibrate the baselines based on crude mortality rates from a major Kenyan insurer. Comparing the gamma-exponentiated Weibull with the non-central gamma-exponentiated Weibull models shows that the non-central gamma provides a good fit to the real life data-set and is therefore recommended for valuation.

The new odd Lindley-G Power Series Class of distributions: theory, properties and applications

2024-11-26T05:27:58+00:00

We propose a new generalized class of distributions called the odd Lindley-G Power Series (OL-GPS) family of distributions and a special class, namely, odd Lindley-Weibull power series (OL-WPS) family of distributions. We also derive the structural properties of the OL-GPS family of distributions including moments, order statistics, R´enyi entropy, mean and median deviations, Bonferroni and Lorenz curves, and maximum likelihood estimates. Sub-models of the special cases were also obtained together with their structural properties. A simulation study to examine the consistency of the maximum likelihood estimators for each parameter is presented. Finally, real data examples are presented to illustrate the applicability and usefulness of the proposed model.

A goodness-of-fit test based on Kendall’s process: Durante’s bivariate copula models

2024-11-26T05:45:09+00:00

The proposed goodness-of-fit testing procedures for copula models are fairly recent. The new test statistics or omnibus tests are functional of an empirical process motivated by the theoretical and empirical versions of Kendall’s or Spearman’s dependence function. In this paper, we propose a fitting procedure for a symmetric and flexible copula model with a non-zero singular component using the Kendall process. The conditions under which this empirical process weakly converges are satisfied. Using a parametric bootstrap method that allows to compute approximate p-values, it is empirically shown that tests based on the Cram´ervon Mises distance keeps the prescribed value for the nominal level under the null hypothesis. Simulation studies that demonstrate the power of the fit test are presented.

Applying of the Extreme Value Theory for determining extreme claims in the automobile insurance sector: Case of a China car insurance

2024-11-26T05:54:35+00:00

According to the Chinese Health Statistics Yearbook, in 2005, the number of traffic accidents was 187781 with total direct property losses of 103691.7 (10000 Yuan). This research aims to fill the gap in the literature by investigating the extreme claim sizes not only for the entire portfolio. This empirical study investigates the behavior of the upper tail of the claim size by class of policyholders.

A stepwise procedure for toxicity studies based on ratio of two means

2024-11-26T06:06:25+00:00

This paper proposes a stepwise confidence set procedure for identifying equivalence or safety of compounds in a toxicity study under heteroscedasticity of variances for a normally distributed data. The problem of statistical methodology for drug safety is the control of the familywise error rate (FWER). Hence, we construct a confidence set procedure for toxicological evaluation and incorporating the partitioning principle with a case of heteroscedascity of variances under normal assumption. Our simulation studies demonstrated that the power of the procedures for heterogeneity of variances increases with increasing in ratio of means.