Bonferroni Curve and the related statistical inference

Pundir, Sudesh; Arora, Sangeeta; Jain, Kanchan

doi:10.1016/j.spl.2005.05.024

Cited by 32 publications

(17 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The mean deviations about the mean δ 1 = E(| X − µ (20) with u = p. These curves have significant roles in demography, economics, insurance, medicine and reliability. For details in this aspect, the readers are referred to Pundir et al(2005) and references cited therein.…”

Section: Incomplete Moments Mean Deviations and Lorenz And Benferronmentioning

confidence: 99%

The Generalized Additive Weibull-G Family of Distributions

Hassan¹,

Hemeda²,

Maiti³

et al. 2017

IJSP

View full text Add to dashboard Cite

In this paper, we present a new family, depending on additive Weibull random variable as a generator, called the generalized additive Weibull generated-family (GAW-G) of distributions with two extra parameters. The proposed family involves several of the most famous classical distributions as well as the new generalized Weibull-G family which already accomplished by Cordeiro et al. (2015). Four special models are displayed. The expressions for the incomplete and ordinary moments, quantile, order statistics, mean deviations, Lorenz and Benferroni curves are derived. Maximum likelihood method of estimation is employed to obtain the parameter estimates of the family. The simulation study of the new models is conducted. The efficiency and importance of the new generated family is examined through real data sets.

show abstract

Section: Incomplete Moments Mean Deviations and Lorenz And Benferronmentioning

confidence: 99%

The Generalized Additive Weibull-G Family of Distributions

Hassan¹,

Hemeda²,

Maiti³

et al. 2017

IJSP

View full text Add to dashboard Cite

show abstract

“…The Lorenz and Bonferroni curves are defined by L(p) = ϕ 1 (x p )/µ 1 and B(p) = ϕ 1 (x p )/(pµ 1 ), respectively, where x p = F −1 (p; υ) can be computed numerically by (3.1) for a given probability p. These curves have significant role in economics, reliability, demography, insurance and medicine. Readers are referred to Pescim et al [21] and Pundir et al [22].…”

Section: Incomplete Moments the Sth Incomplete Moment Ofmentioning

confidence: 99%

The Marshall-Olkin Additive Weibull Distribution with Variable Shapes for the Hazard Rate

Afify¹,

Cordeiro²,

Yousof³

et al. 2016

HJMS

View full text Add to dashboard Cite

We introduce and study the Marshall-Olkin additive Weibull distribution in order to allow a wide variation in the shape of the hazard rate, including increasing, decreasing, bathtub and unimodal shapes. The new distribution generalizes at least eleven lifetime models extant in the literature. Various of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, moments of the residual and reversed residual life functions and order statistics are derived. The parameters of the new distribution are estimated by the maximum likelihood method. We illustrate empirically the superiority of the new model over other distributions by means of a real life data set.

show abstract

“…Many papers in the literature deal with the partial order based on the Lorenz curve; whereas some examples of papers dealing with the order based on the Bonferroni curve are: Tarsitano [19], Giorgi and Crescenzi [6], Pundir et al [14]. In analogy to the two aforementioned orderings, Polisicchio and Porro in [12] introduced the order based on the I(p) curve, by the following definition.…”

Section: Features Of the I(p) Curvementioning

confidence: 99%