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Introduction
The word kurtosis comes from a Greek word meaning humped. In statistics Authentic Budda Baker Jersey , it refers to the degree of flatness or peakness in the region about the mode of a frequency curve. Two or more distributions may have identical average, variation and skewness, but they may show different degrees of concentration of values of observations around the mode Authentic Haason Reddick Jersey , and hence may show different degrees of peakness of the hump of the distribution. Kurtosis is the 4th central moment. This is the peakness of a distribution. It measures the extent to which the data are distributed in the tails versus the center of the distribution. There are three types of peaks.
o Leptokurtic- very peaked
o Platykurtic relatively flat
o Mesokurtic in between
Mesokurtic
A frequency curve that is a normal curve. When the distribution is normally distributed, its kurtosis equals 3 and it is said to be Mesokurtic.
Leptokurtic
A frequency curve that is more peaked than the normal curve. When the distribution is less spread out than normal, its kurtosis is greater than 3 and it is said to be leptokurtic.
Platykurtic
A frequency curve that is flat-topped than the normal curve. When the distribution is more spread out than normal Authentic Chase Edmonds Jersey , its kurtosis is less than 3 and it is said to be Platykurtic.
Calculation of Kurtosis
The Mesokurtic, leptokurtic and Platykurtic are qualitative and subjective. The kurtosis of a set of data is measured with the following statistic.
Collectively, the variance (s2) Authentic Mason Cole Jersey , skew (s3), and kurtosis (s4) describe the shape of the distribution
Excess Kurtosis
The larger or smaller value of the kurtosis, the more peaked is the density function. Excess kurtosis measures the degree to which a density function is more or less peaked relative to a standard normal distribution Authentic Christian Kirk Jersey , which has kurtosis equal to 3. The excess kurtosis measure is centered such that it equals 0 for the standard normal distribution. A probability density that has positive excess kurtosis is referred to as being leptokurtic. If excess kurtosis is negative the probability density is referred to as being Platykurtic. If excess kurtosis is zero, so that the probability density has the same excess kurtosis measure as a standard normal distribution, it is referred to as being Mesokurtic.
Conclusion
Kurtosis is derived from the fourth moment. It captures the heaviness or weight of the tails relative to the center of the distribution. Kurtosis measures heavy tailed or light tailed relative to the normal distribution. A heavy-tailed distribution has more values in the tails than the normal distribution Authentic Patrick Peterson Jersey , and will have a negative kurtosis. A light-tailed distribution has more values in the centre than the normal distribution and will have a positive kurtosis. Kurtosis shapes of distributions are generally recognized with various labels and associated kurtosis statistics.
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