Estimation of P[Y < X] for generalized exponential distribution

By Debasis Kundu, Rameshwar D. Gupta. 2005

323 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/291cb185bf7749289c65d4e243b087e299e1dd14

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In Statistics and Probability

Citations in the corpus

Estimation of P(X>Y) with Topp–Leone distribution (2013, background): “Many authors assumed that X and Y belong to a certain family of probability distributions with unknown parameters and then considered the estimation problem of the reliability P, for example, the exponential distribution [1–4], uniform distribution [3], generalized exponential distribution [5], gene”
Burr-XII Distribution Parametric Estimation and Estimation of Reliability of Multicomponent Stress-Strength (2015, background): “…were considered by several authors for different distributions (Enis and Geisser (1971), Downtown (1973), Awad and Gharraf (1986), McCool (1991), Nandi and Aich (1994), Surles and Padgett (1998), Raqab and Kundu (2005), Kundu and Gupta (2005, 2006), Raqab et al. (2008), and Kundu and Raqab (2009)).”
Stress-strength reliability of Weibull distribution based on progressively censored samples (2011, methodology): “Now, we approximate the likelihood equation analogously to Kundu and Gupta (2006). It is based on the fact that if the random variable X has W (α,θ ), then V = lnX , has the extreme value distribution with pdf as”
Estimation of reliability of multicomponent stress–strength for a Kumaraswamy distribution (2017, methodology): “Later, Nadar et al. (2014) studied the estimation of the reliability R = P(Y < X ) when X and Y are independent random variables following the Kumaraswamy distribution with different parameters.”
Classical and Bayesian Estimation of Reliability in Multicomponent Stress-Strength Model Based on Weibull Distribution (2015, methodology): “When the X and Y are independent and follow the generalized exponential, Weibull, three-parameter Weibull and Kumaraswamy distributions, the estimation of R was studied by Kundu & Gupta (2005), Kundu & Gupta (2006), Kundu & Raqab (2009) and Nadar, Kizilaslan & Papadopoulos (2014), respectively.”
Classical and Bayesian estimation of $$P(X<Y)$$P(X<Y) using upper record values from Kumaraswamy’s distribution (2014, methodology): “Moreover, the comparison of the Shannon information was considered by Madadi and Tata (2011) based on records and random samples. A random variable X said to have a Kumaraswamy distribution, denoted by X ∼ K um(a, b), if its cdf is F(x; a, b) = 1 − (1 − xa)b, 0 < x < 1, (1) and hence the pdf is give”
Classical and Bayesian estimation of P(Y < X) for Kumaraswamy's distribution (2014, methodology): “The estimation of P(Y < X) was studied for the Burr-type III by Mokhlis [31], for the Weibull by Kundu and Gupta [32], for the generalized exponential by Kundu and Gupta [33] and for the generalized Pareto by Rezaei et al. [34].”
Estimation of Reliability in Multicomponent Stress-strength Based on Generalized Exponential Distribution (2014, unknown): “…authors assuming various lifetime distributions for the stress-strength random variates (Enis & Geisser, 1971; Downtown, 1973; Awad & Gharraf, 1986; McCool, 1991; Nandi & Aich, 1994; Surles & Padgett, 1998; Raqab & Kundu, 2005; Kundu & Gupta, 2005, 2006; Raqab, et al., 2008; Kundu & Raqab, 2009).”
Estimation of P(Y < X) for the Three-Parameter Generalized Exponential Distribution (2008, background): “Recently, Kundu and Gupta (2005) and Raqab and Kundu (2005) considered the estimation of R for the two-parameter GE distribution and scaled Burr Type X distribution, respectively.”
Estimation of P[Y<X]P[Y<X] for generalized Pareto distribution (2010, methodology): “So, we adopt the suggestion of Congdon (2001, p. 20) and Kundu and Gupta (2005), i.e., choose a1 =a2 =b1 =b2 =0.0001.”
Generalized exponential distribution: Existing results and some recent developments (2007, methodology): “α2 can be obtained in explicit forms in terms of MLE of λ, same as provided in (13), see [19] for details.”