Computing the moments of order statistics from nonidentical random variables

By H. M. Barakat, Y. H. Abdelkader. 2004

123 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/def19785059af2e86668fe7b119a7ecff6fa87ea

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In Artificial Intelligence

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Citations in the corpus

Explicit expressions for moments of order statistics (2008, methodology): “To find the moment of X r : n , we use the following result due to Barakat and Abdelkader ( 2004 ): where where F i t (·) is the cdf of X i t given by Setting x = y /(1 + y ) and using the series expansion one can express I j ( k ) in ( 11 ) as Us”
The McDonald Weibull model (2014, methodology): “Alternatively, we obtain another explicit expression for these moments using a result due to Barakat and Abdelkader [31] applied to the i.”
The Burr XII power series distributions: A new compounding family (2015, unknown): “An explicit expression for the sth moment Xi:m can also be obtained from a result due to Barakat and Abdelkader (2004) E ( Xsi:m ) = s m∑ j=m−i+1 (−1)j−m+i−1 ( j − 1 m − i )( m j )∫ ∞ 0 xs−1S(x, θ, c, k)j dx (3.13) = s m∑ j=m−i+1 (−1)j−m+i−1 C(θ)j ( j − 1 m − i )( m j )∫ ∞ 0 xs−1C [ θ ( 1 + xc)−k]j…”
The Kumaraswamy Burr XII distribution: theory and practice (2013, methodology): “[24] H.M. Barakat and Y.H. Abdelkader, Computing the moments of order statistics from nonidentical random variables, Stat.”
The Kumaraswamy Generalized Half-Normal Distribution for Skewed Positive Data (2012, methodology): “We use the formula for the sth moment due to Barakat and Abdelkader (2004) applied to the independent and identically distributed case, subject to existence, E(X i:n) = s n ∑ j=n−i+1 (−1)j−n+i−1 ( j − 1 n− i )( n j ) Ij(s), (34)”
The Weibull-geometric distribution (2008, methodology): “An alternative expression to Equation (11) can be obtained by using a result due to Barakat and Abdelkader [6], which is valid for |p| ≤ 1.”
A new lifetime model with decreasing failure rate (2010, methodology): “For this, we use a result due to Barakat and Abdelkader [15] and obtain E(Xri:n) = r n∑ k=n−i+1 (−1)k−n+i−1 ( k − 1 n − i )( n k ) [ θ2(1 + θ)−1 1 + 3θ + θ2 ]k × ∫ ∞ 0 xr−1e−βkx {3 + θ − (2 + θ)(1 + θ)−1e−βx}k {1 − (1 + θ)−1e−βx}2k dx. Applying Equation (6) and binomial expansion to the terms {1 − (”
The Kumaraswamy modified Weibull distribution: theory and applications (2014, methodology): “Alternatively, we can obtain another explicit formula for these moments using a result due to Barakat and Abdelkader [29] applied to the i.”
A new family of generalized distributions (2011, methodology): “We use the formula for the sth moment due to Barakat and Abdelkader [16] applied to the independent and identically distributed case, subject to existence,”
The complementary exponential power series distribution (2013, methodology): “The moments of the CEPS distribution order statistics are obtained by using a result due to Barakat and Abdelkader (2004) applied to the independent and identically distributed (i.i.d.) case, leading to E[Xri:n; θ,β] = r n∑ k=n−i+1 (−1)k−n+i−1 ( k − 1 n − i )( n k )∫ ∞ 0 xr−1Sk(x;β,p)dx = r…”
The exponentiated generalized gamma distribution with application to lifetime data (2011, methodology): “Alternatively, the moments of the order statistics of the EGG distribution can be obtained using the following expansion due to Barakat and Abdelkader [25] applied to the independent and identically distributed case”
The generalized inverse Weibull distribution (2011, background): “An alternative formula for this moment ( Barakat and Abdelkader 2004 )i s”