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math.PR2020
Monotonicity properties of the gamma family of distributions
Iosif Pinelis
For real , let denote a random variable with the gamma distribution with parameters and . Then is increasing in for each real ; no…
math.PR2020
Monotonicity properties of the Poisson approximation to the binomial distribution
Iosif Pinelis
Certain monotonicity properties of the Poisson approximation to the binomial distribution are established. As a natural application of these results, exact (rather than approximate…
math.ST2020
Monotonicity preservation properties of kernel regression estimators
Iosif Pinelis
Three common classes of kernel regression estimators are considered: the Nadaraya--Watson (NW) estimator, the Priestley--Chao (PC) estimator, and the Gasser--Müller (GM) estimator.…