New series representation for the trivariate non-central chi-squared distribution

Notes on the chi-squared distribution

MISS DISTANCE – GENERALIZED VARIANCE NON - CENTRAL CHI DISTRIBUTION Ken

In many current practical applications, the probability of collision is often considered as the most meaningful criterion for determining the risk to a spacecraft. However, when the miss distance is very small (say 100 m or less), the collision probability may not comfortably serve well as the only metric for measuring the risk. In these cases, it is also important to know the statistics of the...

Information Divergence is more chi squared distributed than the chi squared statistics

For testing goodness of fit it is very popular to use either the χ-statistic or G-statistics (information divergence). Asymptotically both are χ-distributed so an obvious question is which of the two statistics that has a distribution that is closest to the χ-distribution. Surprisingly, when there is only one degree of freedom it seems like the distribution of information divergence is much bet...

CHI-Squared Test of Independence

Chi-square (X) test is a nonparametric statistical analyzing method often used in experimental work where the data consist in frequencies or ‘counts’ – for example the number of boys and girls in a class having their tonsils out – as distinct from quantitative data obtained from measurement of continuous variables such as temperature, height, and so on. The most common use of the test is to ass...

Chi-squared components for tests of fit and improved models for the grouped exponential distribution

We consider testing for an exponential distribution with unspecified rate parameter when it is only possible to observe the counts in groups with boundaries specified before sighting the data. On the basis of a size and power study we recommend that tests of fit for the exponential distribution be based on the Anderson-Darling statistic and the SW2 statistic recommended by Gulati and Neus (2001...