Approximating the Cumulative Chi-Square Distribution and its Inverse

Abstract

This paper proposes an approximation to the cumulative chi‐square distribution and its inverse. The approximation is simple for use on a hand calculator and its accuracy is quite satisfactory for many practical purposes.

Exploring How to Simply Approximate the P-value of a Chi-squared Statistic

“…More tables can be found by considering Khamis and Rudert (1965). Alternative simple procedures for approximating the p-value of a chi-squared statistic can also be found in Terrell (1984) and Lin (1988). The approach that Lin (1988) takes is based on the approximation of the chi-squared quantile proposed by Fisher (1928).…”

“…Alternative simple procedures for approximating the p-value of a chi-squared statistic can also be found in Terrell (1984) and Lin (1988). The approach that Lin (1988) takes is based on the approximation of the chi-squared quantile proposed by Fisher (1928). While these approximations have been shown to be very effective, they don't lend themselves to such simplicity where anything but statistical, or mathematical, computer packages can be used to approximate the p-value.…”

Obtaining confidence intervals for Cpk using percentiles of the distribution of Ĉp

“…For sample sizes of at least 30 Lin [8] claims a maximum relative error of less than 2%. We have written a PASCAL program to calculate the approximation given by Lin [8]. The program is used to generate the values c L and c U in our example and appears in the Figure 3.…”

“…Now since C pk is bounded, as n gets large this probability approaches 0.0027 + Since Y =Ĉ p /C p , its distribution and percentile values are readily available. Hoffman [7] has looked at the generation of exact values in the small sample size case and suggests for larger sample sizes the use of an approximation to the inverse chi-square by Lin [8]. For sample sizes of at least 30 Lin [8] claims a maximum relative error of less than 2%.…”

“…Hoffman [7] has looked at the generation of exact values in the small sample size case and suggests for larger sample sizes the use of an approximation to the inverse chi-square by Lin [8]. For sample sizes of at least 30 Lin [8] claims a maximum relative error of less than 2%. We have written a PASCAL program to calculate the approximation given by Lin [8].…”