Sunoj, S M; Sankaran, P G(Elsevier, March 3, 2012)
[+]
[-]
Abstract:
Quantile functions are efficient and equivalent alternatives to distribution functions
in modeling and analysis of statistical data (see Gilchrist, 2000; Nair and Sankaran,
2009). Motivated by this, in the present paper, we introduce a quantile based Shannon
entropy function. We also introduce residual entropy function in the quantile setup and
study its properties. Unlike the residual entropy function due to Ebrahimi (1996), the
residual quantile entropy function determines the quantile density function uniquely
through a simple relationship. The measure is used to define two nonparametric classes
of distributions
Description:
Statistics and Probability Letters 82 (2012) 1049–1053
Sunoj, S M; Asok, Nanda K; Sankaran, P G(Elsevier, October 4, 2012)
[+]
[-]
Abstract:
Di Crescenzo and Longobardi (2002) introduced a measure of uncertainty in past lifetime
distributions and studied its relationship with residual entropy function. In the present
paper, we introduce a quantile version of the entropy function in past lifetime and study
its properties. Unlike the measure of uncertainty given in Di Crescenzo and Longobardi
(2002) the proposed measure uniquely determines the underlying probability distribution.
The measure is used to study two nonparametric classes of distributions. We prove
characterizations theorems for some well known quantile lifetime distributions
Description:
Statistics and Probability Letters 83 (2013) 366–372
Sunoj, S M; Unnikrishnan Nair, N; Sankaran, P G(Elsevier, December 1, 2012)
[+]
[-]
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)
[+]
[-]
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
Sunoj, S M; Asok, Nanda K; Sankaran, P G(Elsevier, December 4, 2013)
[+]
[-]
Abstract:
In the present paper, we introduce a quantile based Rényi’s entropy function and its residual
version. We study certain properties and applications of the measure. Unlike the residual
Rényi’s entropy function, the quantile version uniquely determines the distribution
Description:
Statistics and Probability Letters 85 (2014) 114–121
Lower partial moments plays an important role in the analysis of risks and
in income/poverty studies. In the present paper, we further investigate its importance
in stochastic modeling and prove some characterization theorems arising out of it. We
also identify its relationships with other important applied models such as weighted
and equilibrium models. Finally, some applications of lower partial moments in
poverty studies are also examined
Description:
METRON - International Journal of Statistics
2008, vol. LXVI, n. 2, pp. 223-242
In this paper, we study some dynamic generalized information measures between a
true distribution and an observed (weighted) distribution, useful in life length studies. Further,
some bounds and inequalities related to these measures are also studied
Sunoj, S M; Maya, S S(Taylor & Francis, August 19, 2006)
[+]
[-]
Abstract:
In this article we introduce some structural relationships between weighted and
original variables in the context of maintainability function and reversed repair rate.
Furthermore, we prove some characterization theorems for specific models such as
power, exponential, Pareto II, beta, and Pearson system of distributions using the
relationships between the original and weighted random variables
Description:
Communications in Statistics—Theory and Methods, 35: 223–228, 2006
Sunoj, S M; Sreejith, T B(Taylor & Francis, March 12, 2012)
[+]
[-]
Abstract:
Recently, reciprocal subtangent has been used as a useful tool to describe the
behaviour of a density curve. Motivated by this, in the present article we extend
the concept to the weighted models. Characterization results are proved for models
viz. gamma, Rayleigh, equilibrium, residual lifetime, and proportional hazards. An
identity under weighted distribution is also obtained when the reciprocal subtangent
takes the form of a general class of distributions. Finally, an extension of reciprocal
subtangent for the weighted models in the bivariate and multivariate cases are
introduced and proved some useful results
Description:
Communications in Statistics—Theory and Methods, 41: 1397–1410, 2012