Weighted.Desc.Stat (version 1.0)

w.r: weighted Pearson's correlation coefficent

Description

Assume that $x=(x_1, x_2, \cdots , x_n)$ is the observed value of a random sample from a fuzzy population. In classical and usual random sample, the degree of belonging $x_i$ into the random sample is equal to 1, for $1 \leq i \leq n$. But considering fuzzy population, we denote the degree of belonging $x_i$ into the fuzzy population (or into the observed value of random sample) by $\mu_i$ which is a real-valued number from [0,1]. Therefore in such situations, it is more appropriate that we show the observed value of the random sample by notation $ \{ (x_1, \mu_1), (x_2, \mu_2), \cdots , (x_n, \mu_n) \} $ which we called it real-valued fuzzy data. The goal of w.r function is computing the Pearson's correlation coefficent (or, the weighted Pearson's correlation coefficent) between two vector-valued data sets $x_1, \cdots , x_n$ and $y_1, \cdots , y_n$ based on real-valued fuzzy data $ \{ (x_1, \mu_1), \cdots , (x_n, \mu_n) \} $ and $ \{ (y_1, \mu_1), \cdots , (y_n, \mu_n) \} $ by formula $ r = \frac{s_{xy}}{s_x s_y}.$

Usage

w.r(x, y, mu)

Arguments

x, y

Two vector-valued numeric data sets which you want to compute the weighted Pearson's correlation coefficent between them.

mu

A vector of weights. The length of this vector must be equal to the length of data sets and each element of it is belongs to interval [0,1].

Value

The weighted correlation coefficent between two vectors x and y, by considering weights vector mu, is numeric or a vector of length one.

Warning

The length of x, y and mu must be equal. Also, each element of mu must be in interval [0,1].

Examples

x <- c(1:10)
y <- c(2, 7, 0.8, -1, 3, 4, 8, 13, 0, 12)
mu <- c(0.9, 0.7, 0.8, 0.7, 0.6, 0.4, 0.2, 0.3, 0.0, 0.1)
w.r(x, y, mu)

## The function is currently defined as
function(x, y, mu)  w.cov(x,y,mu) / (w.sd(x,mu) * w.sd(y,mu))