Distributions

Distributions and its properties

Mahesha Godekere Distribution

Observing the distribution and their characteristics have particular importance in statistics. Distributions describes

  1. the data
  2. central tendency behaviour
  3. dispersion
  4. identify clusters, peaks and gaps

Normal Distribution

The normal distribution, also known as the Gaussian or standard normal distribution, is the distribution that all of its values in a symmetrical fashion, and most of the results are situated around the distribution mean.

Normally distribution is perfectly symmetric around its mean. Since the normally distribution is symmetric around its mean, the measures of central tendency, Mode, Median and Mean have the following relationship.

mode = median = mean

A normally distributed curve has zero skewness as it is perfectly symmetric around its mean.

Normal Distribution Intuition using Python


Click to view Gist...

Skew Distribution

Skewness is a measure of the asymmetry of the distribution. The skewness value can be positive or negative, or even undefined.

In positively skewed distributions, samples are concentrated towards left of the distribution and has the following central tendency relationship.

mode > median > mean

In negatively skewed distributions, samples are concentrated towards right of the distribution and has the following central tendency relationship.

mode < median < mean

Skewed Distribution Intuition using Python


Click to view Gist...

Co-efficients of Skewness

Skewness can be calculated for a dataset as follows:

Skewness = \( \frac {μ - mode}{σ}\)
Skewness = \( \frac {μ - median}{σ}\)
Skewness = \( \frac {Q1 + Q3 - 2Q2}{Q3 - Q1}\)

If Skewness = 0, the distribution is symmetric
If Skewness < 0, the distribution is negatively skewed or left skewed
If Skewness > 0, the distribution is positively skewed or right skewed