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We prove a characterization of Pareto variable based on quantiles when conditional distribution above a threshold is considered. A similar characterization for
exponential distribution is also obtained. The results are extended to discretized random variables. For some well known distributions, effect of conditioning the
variable crossing a threshold on quantiles is investigated. The results are further extended to bivariate exponential and
bivariate Pareto type models those are relevant to explain Lifestyle data.
Applications of the results are made in estimation of conditional quantiles.
Pareto model for excess of flood-peaks of a river seems to be satisfactory
with high threshold values. Applications are also made on Yam-yield, wind speed data of high energy due to extratropical cyclones in coastal regions
and worldwide earth-tremor data.
This talk, which is fifth in a series, is partly based on a theory cum
applied problem arising in the ongoing SMU project "Growth curve estimation in restricted set-up" at ISI Giridih.
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