The Kurtosis Calculator helps you measure the "tailedness" of your data distribution - how heavy or light the tails are compared to a normal distribution. This can reveal important patterns in your data, such as whether extreme values occur more frequently than expected. For example, in financial analysis, high kurtosis could indicate a higher risk of extreme market movements.
Need a quick calculation? Enter your numbers below:
Kurtosis is a measure of the "tailedness" of a probability distribution. It quantifies how heavy the tails of a distribution are compared to a normal distribution.
Sample Kurtosis:
Where:
The following examples illustrate how kurtosis affects the shape of a distribution.
Kurtosis ≈ 0
Characteristics: Moderate peak height and tail weight, typical of normal distribution
Similar to normal distribution with balanced tails.
Kurtosis > 0
Characteristics: Taller peak with more concentration of data, thicker tails indicating more extreme values
Higher peak and heavier tails than normal distribution.
Kurtosis < 0
Characteristics: Flatter peak with more even spread of data, thinner tails indicating fewer extreme values
Lower peak and lighter tails than normal distribution.
Use the kurtosis() function from the moments package to calculate kurtosis.
library(tidyverse)
library(moments)
tips <- read.csv("https://raw.githubusercontent.com/plotly/datasets/master/tips.csv")
kurtosis(tips$tip) # 6.549552
# histogram with density
ggplot(tips, aes(x = tip)) +
geom_histogram(aes(y = after_stat(density)), binwidth = 0.5, fill = "darkblue", alpha = 0.7) +
geom_density(adjust=1.5, color = "red", linewidth = 1) + # the adjust parameter controls the smoothness of the density curve
geom_vline(aes(xintercept = mean(tip)),
linetype = "dashed",
color = "blue",
size = 1) +
geom_vline(aes(xintercept = median(tip)),
linetype = "dotted",
color = "green",
size = 1) +
labs(title = "Histogram and Density of Tip Amounts",
x = "Tip Amount ($)",
y = "Density") +
theme_minimal()The Kurtosis Calculator helps you measure the "tailedness" of your data distribution - how heavy or light the tails are compared to a normal distribution. This can reveal important patterns in your data, such as whether extreme values occur more frequently than expected. For example, in financial analysis, high kurtosis could indicate a higher risk of extreme market movements.
Need a quick calculation? Enter your numbers below:
Kurtosis is a measure of the "tailedness" of a probability distribution. It quantifies how heavy the tails of a distribution are compared to a normal distribution.
Sample Kurtosis:
Where:
The following examples illustrate how kurtosis affects the shape of a distribution.
Kurtosis ≈ 0
Characteristics: Moderate peak height and tail weight, typical of normal distribution
Similar to normal distribution with balanced tails.
Kurtosis > 0
Characteristics: Taller peak with more concentration of data, thicker tails indicating more extreme values
Higher peak and heavier tails than normal distribution.
Kurtosis < 0
Characteristics: Flatter peak with more even spread of data, thinner tails indicating fewer extreme values
Lower peak and lighter tails than normal distribution.
Use the kurtosis() function from the moments package to calculate kurtosis.
library(tidyverse)
library(moments)
tips <- read.csv("https://raw.githubusercontent.com/plotly/datasets/master/tips.csv")
kurtosis(tips$tip) # 6.549552
# histogram with density
ggplot(tips, aes(x = tip)) +
geom_histogram(aes(y = after_stat(density)), binwidth = 0.5, fill = "darkblue", alpha = 0.7) +
geom_density(adjust=1.5, color = "red", linewidth = 1) + # the adjust parameter controls the smoothness of the density curve
geom_vline(aes(xintercept = mean(tip)),
linetype = "dashed",
color = "blue",
size = 1) +
geom_vline(aes(xintercept = median(tip)),
linetype = "dotted",
color = "green",
size = 1) +
labs(title = "Histogram and Density of Tip Amounts",
x = "Tip Amount ($)",
y = "Density") +
theme_minimal()