Sunoj, S M; Unnikrishnan Nair, N(Calcutta: The Association,[1947]-, June , 1999)
[+]
[-]
Abstract:
In this paper, a family of bivariate distributions whose marginals are weighted
distributions in the original variables is studied. The relationship between the failure rates
of the derived and original models are obtained. These relationships are used to provide
some characterizations of specific bivariate models
Description:
Bulletin of the Calcutta Statistical Association,Vol 57 (227-228),pp 179-194
Sunoj, S M; Linu, M N; Navarro, J(Elsevier, June 14, 2011)
[+]
[-]
Abstract:
In this paper, the residual Kullback–Leibler discrimination information measure is
extended to conditionally specified models. The extension is used to characterize some
bivariate distributions. These distributions are also characterized in terms of proportional
hazard rate models and weighted distributions. Moreover, we also obtain some bounds
for this dynamic discrimination function by using the likelihood ratio order and some
preceding results.
Description:
Statistics and Probability Letters 81 (2011) 1594–1598
Sunoj, S M; Navarro, J; Linu, M N(Taylor & Francis, April 14, 2014)
[+]
[-]
Abstract:
In this article, we study some relevant information divergence measures viz. Renyi
divergence and Kerridge’s inaccuracy measures. These measures are extended to conditionally
specifiedmodels and they are used to characterize some bivariate distributions
using the concepts of weighted and proportional hazard rate models. Moreover, some
bounds are obtained for these measures using the likelihood ratio order
Description:
Communications in Statistics—Theory and Methods, 43: 1939–1948, 2014
Sunoj, S M; Sankaran, P G; Maya, S S(Taylor & Francis, December 20, 2006)
[+]
[-]
Abstract:
In this paper, we examine the relationships between log odds rate and various reliability measures
such as hazard rate and reversed hazard rate in the context of repairable systems. We also prove
characterization theorems for some families of distributions viz. Burr, Pearson and log exponential
models. We discuss the properties and applications of log odds rate in weighted models. Further we
extend the concept to the bivariate set up and study its properties.
Sunoj, S M; Sankaran, P G; Maya, S S(Taylor & Francis, September 5, 2008)
[+]
[-]
Abstract:
In this article, we study reliability measures such as geometric vitality function
and conditional Shannon’s measures of uncertainty proposed by Ebrahimi (1996)
and Sankaran and Gupta (1999), respectively, for the doubly (interval) truncated
random variables. In survival analysis and reliability engineering, these measures
play a significant role in studying the various characteristics of a system/component
when it fails between two time points. The interrelationships among these uncertainty
measures for various distributions are derived and proved characterization theorems
arising out of them
Description:
Communications in Statistics—Theory and Methods, 38: 1441–1452, 2009
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; Linu, M N(Taylor & Francis, May 2, 2010)
[+]
[-]
Abstract:
Recently, cumulative residual entropy (CRE) has been found to be a new measure of information that
parallels Shannon’s entropy (see Rao et al. [Cumulative residual entropy: A new measure of information,
IEEE Trans. Inform. Theory. 50(6) (2004), pp. 1220–1228] and Asadi and Zohrevand [On the dynamic
cumulative residual entropy, J. Stat. Plann. Inference 137 (2007), pp. 1931–1941]). Motivated by this finding,
in this paper, we introduce a generalized measure of it, namely cumulative residual Renyi’s entropy,
and study its properties.We also examine it in relation to some applied problems such as weighted and equilibrium
models. Finally, we extend this measure into the bivariate set-up and prove certain characterizing
relationships to identify different bivariate lifetime models
Sunoj, S M; Unnikrishnan Nair, N(Taylor & Francis, August 24, 2002)
[+]
[-]
Abstract:
In this paper the class of continuous bivariate distributions that has form-invariant weighted distribution with weight
function w(x1, x2) ¼ xa1
1 xa2
2 is identified. It is shown that the class includes some well known bivariate models.
Bayesian inference on the parameters of the class is considered and it is shown that there exist natural conjugate
priors for the parameters
Sunoj, S M; Sankaran, P G(Springer, August 6, 2002)
[+]
[-]
Abstract:
In this paper, we study the relationship between the failure rate and the
mean residual life of doubly truncated random variables. Accordingly, we
develop characterizations for exponential, Pareto 11 and beta distributions.
Further, we generalize the identities for fire Pearson and the exponential
family of distributions given respectively in Nair and Sankaran (1991) and
Consul (1995). Applications of these measures in file context of lengthbiased
models are also explored
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