Section 11.3 ni n P

NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT

1103-40-5118 2 March 1956

NBS REPORT

4564

SOME FORMULAS FOR COMPUTING PROBABILITIES

FOR COMMON STATISTICS

by

J 8 Lieblein and J. M e Cameron

U. $. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

The publication, repri Approved for public release by the

unless permission ts ob director of the National Institute of

25 ,d.c. Suchpermis Standards and Technology (NIST)

tally prepared If that 0 n October 9, 2015

part, is prohibited

lards, Washington

t has been specif!-

rt for its own use,

SOME FORMULAS FOR COMPUTING PROBABILITIES

FOR COMMON STATISTICS

by

J. Lieblein and J. M. Cameron

This note gives formulas for computing the probability that

a random variable will exceed a specified value in the case of

the F, t, X

2

, and normal distribution. These formulas were

taken or adapted from standard statistical text books and from

the volumes of the Bateman Manuscript Project referenced herein

as follows:

[1] Higher Transcendental Functions, Vol. 1

[2] Higher Transcendental Functions, Vol. 2.

Most of those from the latter source are new or not well-known

to statisticians. As many such formulas as conveniently available were compiled for the purpose of developing computational

techniques suitable to electronic or punch card machines. It

was considered desirable to preserve them even though they are

not in regular publishable form. For convenience, some of the

well-known classical relationships are also given.
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