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What are the differences between a platykurtic a mesokurtic and a leptokurtic distribution?
The kurtosis of a distribution is defined as the fourth central moment divided by the square of the second central moment. Unfortunately, this browser converts Greek characters to the Roman alphabet so I cannot use standard forms of equations but: Suppose that for a random variable X, E(X) = m (mu) and E[(X - E(X))2] = V = s2 (sigma-squared) then Kurtosis = E[(X - E(X))4]/s4. Excess Kurtosis is then Kurtosis - 3. If excess kurtosis < 0 the distribution is platykurtic. They have a peak that is lower than the Normal: the peak is flat and broad. The tails of the distribution are narrow. Uniform distributions are platykurtic. A mesokurtic distibution has excess kurtosis = 0. The Gaussian (Normal) distribution - whatever its parameters - is mesokurtic. The binomial with probability of success close to 1/2 is also considered to be mesokurtic. If excess kurtosis is > 0 the distribution is leptokurtic. Leptokurtic distributions have a high and narrow peak. A good example is the Student's t distribution.
Define skewness and kurtosis?
Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point. Kurtosis is a measure of whether the data are peaked or flat relative to a normal distribution. See related link. By doing a search on the internet, you can find more examples.
What are the formulas in probability?
There are many, many formulae:for different probability distribution functions,for cumulative distribution functions,for moment generating functions,for means, variances, skewness, kurtosis and higher moments.There are many, many formulae:for different probability distribution functions,for cumulative distribution functions,for moment generating functions,for means, variances, skewness, kurtosis and higher moments.There are many, many formulae:for different probability distribution functions,for cumulative distribution functions,for moment generating functions,for means, variances, skewness, kurtosis and higher moments.There are many, many formulae:for different probability distribution functions,for cumulative distribution functions,for moment generating functions,for means, variances, skewness, kurtosis and higher moments.
Does a normal probability distribution include a bimodal distribution?
No, the normal distribution is strictly unimodal.
Is normal distribution also a probability distribution?
Yes. When we refer to the normal distribution, we are referring to a probability distribution. When we specify the equation of a continuous distribution, such as the normal distribution, we refer to the equation as a probability density function.
