w.mean {Weighted.Desc.Stat} | R Documentation |
weighted mean
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.mean function is computing the mean (or, the weighted mean) value of x_1, \cdots , x_n
based on real-valued fuzzy data \{ (x_1, \mu_1), \cdots , (x_n, \mu_n) \}
by formula
\bar{x} = \frac{\sum_{i=1}^{n} \mu_i x_i}{\sum_{i=1}^{n} \mu_i}.
Usage
w.mean(x, mu)
Arguments
x |
A vector-valued numeric data which you want to compute its weighted mean. |
mu |
A vector of weights. The length of this vector must be equal to the length of data and each element of it is belongs to interval [0,1]. |
Value
The weighted mean of the vector x, by considering weights vector mu, is numeric or a vector of length one.
Warning
The length of x and mu must be equal. Also, each element of mu must be in interval [0,1].
Author(s)
Abbas Parchami
Examples
x <- c(1:10)
mu <- c(0.9, 0.7, 0.8, 0.7, 0.6, 0.4, 0.2, 0.3, 0.0, 0.1)
w.mean(x, mu)
## The function is currently defined as
function(x, mu) sum( mu*abs(x-w.mean(x,mu)) ) / sum(mu)