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September, 1958 Bounds for Mills' Ratio for the Type III Population
A. V. Boyd
Ann. Math. Statist. 29(3): 926-929 (September, 1958). DOI: 10.1214/aoms/1177706554


Cohen [1] and Des Raj [2] have shown that in estimating the parameters of truncated type III populations, it is necessary to calculate for several values of $x$ the Mills ratio of the ordinate of the standardized type III curve at $x$ to the area under the curve from $x$ to $\infty$. Des Raj [3] has also noted that for large values of $x$ the existing tables of Salvosa [4] are inadequate for this purpose and he has found lower and upper bounds for the ratio. The object of this note is to improve these bounds, by obtaining monotonic sequences of lower and upper bounds through the use of continued fractions.


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A. V. Boyd. "Bounds for Mills' Ratio for the Type III Population." Ann. Math. Statist. 29 (3) 926 - 929, September, 1958.


Published: September, 1958
First available in Project Euclid: 27 April 2007

zbMATH: 0090.36405
MathSciNet: MR100308
Digital Object Identifier: 10.1214/aoms/1177706554

Rights: Copyright © 1958 Institute of Mathematical Statistics

Vol.29 • No. 3 • September, 1958
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