Inthis paper,we define partial moments for a univariate continuous random
variable. A recurrence relationship for the Pearson curve using the partial moments is
established. The interrelationship between the partial moments and other reliability
measures such as failure rate, mean residual life function are proved. We also prove
some characterization theorems using the partial moments in the context of length
biased models and equilibrium distributions
Description:
METRON - International Journal of Statistics
2004, vol. LXII, n. 3, pp. 353-362
Sunoj, S M; Unnikrishnan Nair, N; Sankaran, P G(Elsevier, December 1, 2012)
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Abstract:
Partial moments are extensively used in literature for modeling and analysis of lifetime
data. In this paper, we study properties of partial moments using quantile functions.
The quantile based measure determines the underlying distribution uniquely. We then
characterize certain lifetime quantile function models. The proposed measure provides
alternate definitions for ageing criteria. Finally, we explore the utility of the measure to
compare the characteristics of two lifetime distributions
Description:
Journal of the Korean Statistical Society 42 (2013) 329–342
Sunoj, S M; Unnikrishnan Nair, N; Sankaran, P G(Springer, September 29, 2012)
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Abstract:
Partial moments are extensively used in actuarial science for the analysis
of risks. Since the first order partial moments provide the expected loss in a stop-loss
treaty with infinite cover as a function of priority, it is referred as the stop-loss transform.
In the present work, we discuss distributional and geometric properties of the
first and second order partial moments defined in terms of quantile function. Relationships
of the scaled stop-loss transform curve with the Lorenz, Gini, Bonferroni and
Leinkuhler curves are developed
Description:
Stat Methods Appl (2013) 22:167–182
DOI 10.1007/s10260-012-0213-4