## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 29, Number 3 (1958), 926-929.

### Bounds for Mills' Ratio for the Type III Population

#### Abstract

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.

#### Article information

**Source**

Ann. Math. Statist., Volume 29, Number 3 (1958), 926-929.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177706554

**Digital Object Identifier**

doi:10.1214/aoms/1177706554

**Mathematical Reviews number (MathSciNet)**

MR100308

**Zentralblatt MATH identifier**

0090.36405

**JSTOR**

links.jstor.org

#### Citation

Boyd, A. V. Bounds for Mills' Ratio for the Type III Population. Ann. Math. Statist. 29 (1958), no. 3, 926--929. doi:10.1214/aoms/1177706554. https://projecteuclid.org/euclid.aoms/1177706554