Comparisons of several Pareto distributions based on record values

ABSTRACT

In order to avoid wrong conclusions in any further analysis, it is of importance to conduct a formal comparison for characteristic quantities of the distributions. These characteristic quantities we are familiar with include mean, quantity and reliability function, and so on. In this paper, we consider two tests aiming at the comparisons for function of parameters in Pareto distribution based on record values. They are generalized p-value-based test and parametric bootstrap-based test, respectively. The resulting procedures are easy to compute and are applicable to small samples. A simulation study is conducted to investigate and compare the performance of the proposed tests. A phenomenon we note is that generalized p-value-based test almost uniformly outperforms the parametric bootstrap-based test.

KEYWORDS:

• Generalized p-value
• parametric bootstrap
• Pareto distribution
• record values.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G08
• 62G20

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (11171011), the Natural Science Foundation of Beijing (1102010), Beijing Municipal Commission of Education Foundation (KM201410005011), Program for JingHua Talents in Beijing University of Technology, the Research Fund for the Doctoral Program of Higher Education of China (20131103120027), the Science and Technology Program of Beijing Education Commission (KM201610005020), and the Beijing Natural Science Foundation (1154005).