What is Platykurtic and Leptokurtic distribution?
The term “platykurtic” refers to a statistical distribution in which the excess kurtosis value is negative. The opposite of a platykurtic distribution is a leptokurtic distribution, in which excess kurtosis is positive.
What does a Leptokurtic distribution mean?
kurtosis
Leptokurtic distributions are distributions with positive kurtosis larger than that of a normal distribution. A normal distribution has a kurtosis of exactly three. Therefore, a distribution with kurtosis greater than three would be labeled a leptokurtic distribution.
What is the difference between Leptokurtic Platykurtic and Mesokurtic distribution?
Distributions may be described as mesokurtic, platykurtic, or leptokurtic. Mesokurtic distributions have the same kurtosis as that of the normal distribution, or normal curve, also known as a bell curve. In contrast, a leptokurtic distribution has fatter tails.
What is an example of a Platykurtic distribution?
An example of a platykurtic distribution is the uniform distribution, which does not produce outliers. An example of a leptokurtic distribution is the Laplace distribution, which has tails that asymptotically approach zero more slowly than a Gaussian, and therefore produces more outliers than the normal distribution.
What is Platykurtosis?
Noun. platykurtosis (uncountable) (statistics) The property of having kurtosis less than that of a normal distribution; equivalently, having negative excess kurtosis.
What is skew 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 heavy-tailed or light-tailed relative to a normal distribution.
What is Leptokurtic formula?
The formula for kurtosis is expressed as the ratio of the fourth moment and variance (s2) squared or squared the second moment of the distribution. Mathematically, it is represented as, Kurtosis = n * Σni(Yi – Ȳ)4 / (Σni(Yi – Ȳ)2)2.
How do you determine Leptokurtic?
A leptokurtic distribution has excess positive kurtosis, where the kurtosis is greater than 3. The tails are fatter than the normal distribution.
Is T distribution a Platykurtic?
The T distribution is an example of a leptokurtic distribution. It has fatter tails than the normal (you can also look at the first image above to see the fatter tails). Therefore, the critical values in a Student’s t-test will be larger than the critical values from a z-test.
What does kurtosis mean?
Kurtosis is a measure of the combined weight of a distribution’s tails relative to the center of the distribution. Kurtosis is sometimes confused with a measure of the peakedness of a distribution. However, kurtosis is a measure that describes the shape of a distribution’s tails in relation to its overall shape.
How can you tell if a distribution suffers from Platykurtosis or Leptokurtosis?
K < 3 indicates a platykurtic distribution (flatter than a normal distribution with shorter tails). K > 3 indicates a leptokurtic distribution (more peaked than a normal distribution with longer tails). K = 3 indicates a normal “bellshaped” distribution (mesokurtic). K < 3 indicates a platykurtic distribution.