Abstract
In this paper we define and study the hybrids of exponential families and linear positive operators corresponding to them. These operators include some well-known operators as special cases.
Highlights
We first define the following two auxiliary exponential families: the B-family, and the H-family.Using the families, we define the main object of the paper, namely the Phillips type family
We study some properties B-family, the H-family, the Phillips type family
Pn ( f, x) is transformed into something the modified of the Phillips type operators [1]
Summary
We first define the following two auxiliary exponential families: the B-family, and the H-family.Using the families, we define the main object of the paper, namely the Phillips type family. The exponential family of the discrete distribution with probability mass functions bn,k (x), k = 0,1, ((n,x) are. Parameters, and ∑bn,k (x) = 1 ) is called the B-family if the k =0 following condition holds: b(x). The family of the discrete distribution with probability mass functions bn,k (x) := bk ( y(x))k (ω( y(x)))n. The exponential family of the continuous distributions with prob∞ability density functions hn,k (t) ( (n,k)are parameters, and ∫ hn,k (t)dt = 1) is called the H-family if the following. The family of the continuous distributions with probability density functions. ((n,x) are parameters) is called the Phillips type family. Let the function f by the defined and integrable on R, and let pn (x,t) be the density of a random variable η .. Szasz-Baskakov type operators [3]
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