Relations for reliability measures of weighted distributions

Jain, Kanchan; Singh, Harshinder; Bagai, Isha

doi:10.1080/03610928908830162

Cited by 45 publications

(18 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Under length-biased sampling, the vertical separation diminishes as t increases. Properties of hazards and related functions under biased sampling have been discussed in the literature [2,4,6].…”

Section: Introductionmentioning

confidence: 99%

Fitting parametric frailty and mixture models under biased sampling

Economou

Caroni

2008

Journal of Applied Statistics

View full text Add to dashboard Cite

Biased sampling from an underlying distribution with p.d.f. f(t), t>0, implies that observations follow the weighted distribution with p.d.f. fw(t)=w(t)f(t)/E[w(T)] for a known weight function w. In particular, the function w(t)=tα has important applications, including length-biased sampling (α=1) and area-biased sampling (α=2). We first consider here the maximum likelihood estimation of the parameters of a distribution f(t) under biased sampling from a censored population in a proportional hazards frailty model where a baseline distribution (e.g. Weibull) is mixed with a continuous frailty distribution (e.g. Gamma). A right-censored observation contributes a term proportional to w(t)S(t) to the likelihood; this is not the same as Sw(t), so the problem of fitting the model does not simply reduce to fitting the weighted distribution. We present results on the distribution of frailty in the weighted distribution and develop an EM algorithm for estimating the parameters of the model in the important Weibull-Gamma case. We also give results for the case where f(t) is a finite mixture distribution. Results are presented for uncensored data and for Type I right censoring. Simulation results are presented, and the methods are illustrated on a set of lifetime data.weighted distribution, biased sampling, frailty, finite mixture, Weibull distribution, Burr distribution, Type I right censoring, EM algorithm,

show abstract

Section: Introductionmentioning

confidence: 99%

Fitting parametric frailty and mixture models under biased sampling

Economou

Caroni

2008

Journal of Applied Statistics

View full text Add to dashboard Cite

show abstract

“…Statistical applications of the weighted distributions especially to the analysis of data relating to human populations, ecology, forestry and reliability. Readers may refer to Patil and Rao (1977), Jain et al (1989), Bartoszewicz and Skolimowska (2004) and Belzunce et al (2004) for more details. Suppose that X w and Y w be weighted versions of the random variables X and Y with density functions…”

Section: Proportional Laplace Transform Orders For Weighted Distri-bumentioning

confidence: 99%

Proportional ratios orders based on laplace transforms

Jarrahiferiz¹,

Borzadaran²,

Roknabadi³

2013

Journal of Applied Mathematics, Statistics and Informatics

View full text Add to dashboard Cite

show abstract

“…Jain et al (1989) showed that if the weight function w is increasing and concave and F is IFR, then F also is IFR. Let F be the weighted distribution associated with F .…”

Section: Weighted Distributions With Monotone Failure Ratementioning

confidence: 99%