Statistical Modelling 5 (2005), 343–358
Analyzing lifetime data with long-tailed skewed
distribution: the logistic-sinh family
Kahadawala Cooray
Department of Mathematical Sciences,
University of Nevada,
Las Vegas, NV 89154,
USA
Abstract:
A new two-parameter family of distribution is presented.
It is derived to model the highly
negatively skewed data with extreme observations. The
new family of distribution is referred to as the
logistic-sinh distribution, as it is derived from
the logistic distribution by appropriately replacing an exponential
termwith a hyperbolic sine term.The resulting family provides
not only negatively skewed densities
with thick tails but also variety of monotonic density shapes.
The space of shape parameter, lambda greater
than zero is divided by boundary line of lambda equals one,
into two regions overwhich the hazard function
is, respectively, increasing and bathtub shaped. The maximum
likelihood parameter estimation techniques
are discussed by providing approximate coverage probabilities
for uncensored samples. The advantages of
using the new family are demonstrated and compared by
illustrating well known examples.
Keywords:
bathtub shaped failure rate; coverage probabilities;
goodness-of-fit; increasing failure rate;
Kaplan–Meier curve; right censoring
Downloads:
Example data in zipped archive
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