The first one is to input the dataset and variable. To add the flexibility to the macro, we allow two different ways to input required information. Let X represent given data, and its first four central moments can be calculated by To determine the type of the Pearson distribution and the required parameters of the density function for the chosen type, the only thing we need to know is the first four moments of the data.
PEARSON STANDARD NORMAL TABLE PLUS
Pearson distributions are a family of distributions which consist of seven different types of distributions plus normal distribution (Table 1). Thus, a new program is needed for efficiently computing probability values of Pearson distributions for any given data point and therefore, researchers can utilize the program to conduct more applicable statistical analysis, such as distribution-free hypothesis testing, on data with unknown distributions. Unfortunately, they are little useful in statistical analysis because we have to employ unwieldy second difference interpolation for both skewness √ β 1 and kurtosis β 2 to calculate a probability value of a Pearson distribution corresponding to a given percentage point, such as an observed test statistic in hypothesis testing. There are both extant, old-fashioned in-print tables and contemporary computer programs that provided a means of obtaining percentage points of Pearson distributions corresponding to certain pre-specified percentages (or probability values e.g., 1.0%, 2.5%, 5.0%, etc.). Then, we can compute and use a p-value (or probability value) of the approximated Pearson distribution to make a statistical decision for such distribution-free hypothesis testing. For instance, in hypothesis testing, a sampling distribution of an observed test statistic is usually unknown but the sampling distribution can be fitted into one of Pearson distributions.
Thus, Pearson distributions made statistical analysis possible for any data with unknown distributions. Pearson distributions can be approximated for any data using the first four moments of the data. Most of statistical analysis relies on normal distributions, but this assumption is often difficult to meet in reality. 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 present study develops a SAS/IML 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. 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. Tables of the standardized percentage points of the pearson system of curves in terms of β 1 and β 2. Tables of percentage points of standardized pearson distributions. 1972) and contemporary computer programs (Amos DE, Daniel SL. Biometrika Tables for Statisticians, vol.
There are both extant, old-fashioned in-print tables (Pearson ES, Hartley HO. Thus, Pearson distributions made statistical analysis possible for data with unknown distributions. Any empirical data can be approximated to one of Pearson distributions using the first four moments of the data (Elderton WP, Johnson NL.