APPLICATION OF THE REGULARIZING BAYESIAN APPROACH TO DETERMINING THE LAWS OF THE DISTRIBUTION OF BANK'S RATING VALUES

Determining the rating ratings of banks is important both for the banks themselves and for assessing the state of the entire financial sector of the state. Their compliance with real situations depends on the calculation models used by rating agencies. One of the main stages of calculation in the development of the model is the stage of determining the ranges of estimates. In many methods of rating banks, the ranges are determined by experts and are subjective in nature. In this paper, we propose an algorithm for determining the ranges of rating ratings using the approximation of the distribution laws of the estimated indicators of the model by the Pearson system curves. This approach can significantly improve the accuracy and objectivity of rating assessments

Computing and graphing probability values of pearson distributions: a SAS/IML macro

Background Any empirical data can be approximated to one of Pearson distributions using the first four moments of the data (Elderton WP, Johnson NL. Systems of Frequency Curves. 1969; Pearson K. Philos Trans R Soc Lond Ser A. 186:343–414 1895; Solomon H, Stephens MA. J Am Stat Assoc. 73(361):153–60 1978). Thus, Pearson distributions made statistical analysis possible for data with unknown distributions. There are both extant, old-fashioned in-print tables (Pearson ES, Hartley HO. Biometrika Tables for Statisticians, vol. II. 1972) and contemporary computer programs (Amos DE, Daniel SL. Tables of percentage points of standardized pearson distributions. 1971; Bouver H, Bargmann RE. Tables of the standardized percentage points of the pearson system of curves in terms of β1 and β2. 1974; Bowman KO, Shenton LR. Biometrika. 66(1):147–51 1979; Davis CS, Stephens MA. Appl Stat. 32(3):322–7 1983; Pan W. J Stat Softw. 31(Code Snippet 2):1–6 2009) available for obtaining percentage points of Pearson distributions corresponding to certain pre-specified percentages (or probability values; e.g., 1.0%, 2.5%, 5.0%, etc.), but they are little useful in statistical analysis because we have to rely on unwieldy second difference interpolation to calculate a probability value of a Pearson distribution corresponding to a given percentage point, such as an observed test statistic in hypothesis testing. Results The present study develops a macro program to identify the appropriate type of Pearson distribution based on either input of dataset or the values of four moments and then compute and graph probability values of Pearson distributions for any given percentage points. Conclusions The SAS macro program returns accurate approximations to Pearson distributions and can efficiently facilitate researchers to conduct statistical analysis on data with unknown distributions.

The Pearson and Johnson Systems

This chapter re-examines two of the best-known systems of parametric distributions: the Pearson and the Johnson. It is shown that, in the Pearson system, Pearson Types III and V are boundary embedded models of the main Types I, IV, and VI. A comprehensive way of finding the best type to fit is given using appropriate score statistics to guide a systematic search of all model types, including symmetric boundary models. Maximum likelihood estimation is used and details of its numerical implementation are given. Type IV can be a difficult model to fit. A method is discussed for this model that is reasonably robust, subject to certain restrictions on the parameter values. The same examination is made of the Johnson system where the lognormal, SL family is shown to be an embedded subsystem of both the main subsystems SB and SU. Two real data examples are given.

Characterizations of the Amoroso distribution

Characterizations of the Amoroso distribution based on a simple relationship between two truncated moments are presented. A remark regarding the characterization of certain special cases of the Amoroso distribution based on hazard function is given. We will also point out that a sub-family of the Amoroso family is a member of the generalized Pearson system.