6,227 research outputs found
Properties and Applications of some Distributions derived from Frullani's integral
Frullani's integral dates from 1821, but a probabilistic interpretation of it
has never been made. In this paper, Frullani's integral formula is shown to
result from mixing a lifetime distribution by allowing the logarithm of the
scale factor to be uniformly distributed over a finite range. This gives a
class of long-tailed distributions related to slash distributions, where the
pdf is simply expressed in terms of the survival function of the `parent'
distribution. The resulting survival distributions have all moments finite, and
can exhibit the bimodal hazard functions sometimes seen in practice. A
distribution of this type analogous to the t-distribution is derived, the
corresponding multivariate distributions are given, and two skewed versions of
this distribution are derived. The use of the mixed distributions for inference
is exemplified by fitting them to several datasets. It is expected that there
will be many applications, in health, reliability, telecommunications, finance,
etc.Comment: 6 figure
A new distribution for robust least squares
A new distribution is introduced, which we call the twin-t distribution. This
distribution is heavy-tailed like the t distribution, but closer to normality
in the central part of the curve. Its properties are described, e.g. the pdf,
the distribution function, moments, and random number generation. This
distribution could have many applications, but here we focus on its use as an
aid to robustness. We give examples of its application in robust regression and
in curve fitting. Extensions such as skew and multivariate twin-t
distributions, and a twin ofComment: 29 pages. 5 figures provided at the end of the pape
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