s.combine.stats4 {ldt}

Combine Mean, Variance, Skewness, and Kurtosis This function combines two sets of mean, variance, skewness, and kurtosis and generates the combined statistics.

Description

Combine Mean, Variance, Skewness, and Kurtosis This function combines two sets of mean, variance, skewness, and kurtosis and generates the combined statistics.

Usage

s.combine.stats4(list1, list2)

Arguments

list1

A list representing the first mean, variance, skewness, kurtosis, weight, and count.

list2

A list representing the second distribution (similar to list1).

Details

Assume there are two samples with mean_i, variance_i, skewness_i, and kurtosis_i for i=1,2, this function calculates the mean, variance, skewness, and kurtosis of the combined sample. It does not need the data itself. It is based on population variance, skewness, and kurtosis and calculates the population statistics. Note that the kurtosis is not excess kurtosis.

Value

A list similar to list1.

Examples

n <- 1000 # sample size (increase it for more accurate result)
sample1 <- rchisq(n,3)
sample2 <- rchisq(n,5)

d1 <- list(mean = mean(sample1),
           variance = var(sample1),
           skewness = moments::skewness(sample1),
           kurtosis = moments::kurtosis(sample1),
           count=length(sample1),
           weight = length(sample1))
d2 <- list(mean = mean(sample2),
           variance = var(sample2),
           skewness = moments::skewness(sample2),
           kurtosis = moments::kurtosis(sample2),
           count=length(sample2),
           weight = length(sample2))
c <- s.combine.stats4(d1,d2)

# we can compare the results:
combined <- c(sample1,sample2)
mean_c = mean(combined)
variance_c = var(combined)
skewness_c = moments::skewness(combined)
kurtosis_c = moments::kurtosis(combined)