General results for the Marshall and Olkin's family of distributions
By W. Barreto‐Souza, Artur J. Lemonte, Gauss Moutinho Cordeiro. 2013
57 citations recorded by the source corpus.
Abstract Marshall and Olkin (1997) introduced an interesting method of adding a parameter to a wellestablished distribution. However, they did not investigate general mathematical properties of their family of distributions. We provide for this family of distributions general expansions for the density function, explicit expressions for the moments and moments of the order statistics. Several especial models are investigated. We discuss estimation of the model parameters. An application to a real data set is presented for illustrative purposes.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/178077b3de81bac3969d0ac0d72f2f9e65b46e7f
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In Artificial Intelligence
In Statistics and Probability
- Debasis Kundu
- Miroslav M. Ristic
- Gauss Moutinho Cordeiro
- Biswabrata Pradhan
- Ahmed Z. Afify
- Rameshwar D. Gupta
- Saralees Nadarajah
- Narayanaswamy Balakrishnan
Citations in the corpus
- Marshall-Olkin generalized exponential distribution (2015, methodology): “Similarly for the case θ > 1/2, it can be shown in this case that the n-th moment of a random variable X can be calculated as E(Xn) = α(−1)n θλn ∞∑ k=0 ( 1− 1 θ )k (k + 1) ∂n ∂pn B(α(k + 1), p) ∣∣∣ p=1 , see Barreto-Souza et al. (2013).”