Distribution functions and log-concavity
| Autor: | M. Roters, H. Finner |
|---|---|
| Rok vydání: | 1993 |
| Předmět: | |
| Zdroj: | Communications in Statistics - Theory and Methods. 22:2381-2396 |
| ISSN: | 1532-415X 0361-0926 |
| DOI: | 10.1080/03610929308831156 |
| Popis: | This paper presents a collection of log-concavity results of one-dimensional cumulative distribution functions (cdf's) F(x,ϑ) and the related functions . in both x∈R or x∈Z and θ ∈ Θ. where R denotes the real line and Z the set of integers. We give a review of results available in the literature and try to fill some gaps in this field. It is well-known that log-concavity properties in x of a density f carry over to F. [Fbar]. and Jc in the continuous and discrete case. In addition, it will be seen that the log-concavity of g(y) = f(ey ) in y for a Lebesgue density f with f(x) = 0 for x < 0 implies the log-concavity of F. This criterion applies to many common densities. Moreover, a convex statistic T defined on R" is shown to have a log-concave cdf whenever the underlying n-dimensional Lebesgue density h is log-concave. A slight generalization of the approach in Das Gupta & Sarkar (1984) is used to establish a connection between log-concavity in x of probability densities f or cdf s F and log-concavity of ... |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|