TY - GEN
T1 - An Exact Expression for the Behrens-Fisher Distribution with Applications
AU - Champ, Charles W.
AU - Hu, Fengjiao
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024
Y1 - 2024
N2 - An exact solution is given for the Behrens-Fisher distribution under the independent Normal model. The cumulative distribution function (cdf) and the probability density function (pdf) are expressed as convex combinations of non-central t-distributions cdfs and pdfs, respectively. It is then observed that if the means are equal the distribution depends only on the ratio of the two population variances and the sample sizes. When the means are not equal, the distribution depends on the difference of the two means, the ratio of the two population variances, and the two sample sizes. Some examples are given applying these results.
AB - An exact solution is given for the Behrens-Fisher distribution under the independent Normal model. The cumulative distribution function (cdf) and the probability density function (pdf) are expressed as convex combinations of non-central t-distributions cdfs and pdfs, respectively. It is then observed that if the means are equal the distribution depends only on the ratio of the two population variances and the sample sizes. When the means are not equal, the distribution depends on the difference of the two means, the ratio of the two population variances, and the two sample sizes. Some examples are given applying these results.
KW - Cumulative distribution function
KW - Non-central t distribution
KW - Probability density function
UR - http://www.scopus.com/inward/record.url?scp=85210160439&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-69710-4_9
DO - 10.1007/978-3-031-69710-4_9
M3 - Conference article
AN - SCOPUS:85210160439
SN - 9783031697098
T3 - Springer Proceedings in Mathematics and Statistics
SP - 227
EP - 245
BT - Applied Mathematical Analysis and Computations II - 1st SGMC
A2 - Wanduku, Divine
A2 - Zheng, Shijun
A2 - Chen, Zhan
A2 - Sills, Andrew
A2 - Zhou, Haomin
A2 - Agyingi, Ephraim
PB - Springer
T2 - 1st Southern Georgia Mathematics Conference, SGMC 2021
Y2 - 2 April 2021 through 3 April 2021
ER -