Saturday, October 27, 2018

NOTE ON KURTOSIS



Kurtosis
In probability theory and statistics, Kurtosis is a measure of the tailedness of the probability distribution of a real valued random variable.  In a similar way to the concept of skewness, kurtosis is a descriptor of the shape of a probability distribution and, just as for skewness, there are different ways of quantifying it for a theoretical distribution and curresponding ways of estimating it from a sample from a population.  Depending on the particular measure of kurtosis that is used, there are various interpretations of kurtosis, and of how particular measure should be interpreted.
The standard measure of kurtosis, originating with Karl Pearson, is based on a scaled version of the fourth moment of the data or population.  This number is related to the tails of the distribution, not its peak, hence, the sometimes seen characterization as peakedness is mistaken.  For this measure higher kurtosis is the result of infrequent extreme deviations, as opposed to frequent modestly sized deviations.
The kurtosis of any univariate normal distribution is 3. It is common to compare the kurtosis of a distribution to this value.  Distributions with kurtosis less than 3 are said to be platykurtic, although this does not imply the distribution is "flat-topped" as sometimes reported. Rather, it means the distribution produces fewer and less extreme outliers than does the normal distribution.  An example of a platykurtic distribution is the uniform distribution, which does not produce outliers.  Distributions with kurtosis greater than 3 are said to be leptokurtic. 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.  It is also common practice to use an adjusted version of Pearson's kurtosis, the excess kurtosis, which is the kurtosis minus 3, to provide the comparison to the normal distribution.
Types of Kurtosis
There are three types kurtosis, first one is Mesokurtic, second one is Leptokurtic and third one is Platykurtic.








Figure.1 Types of  Kurtosis
Distribution with zero excess kurtosis are called mesokurtic, or mesokurtotic.  The most prominent example of a mesokurtic distribution is the normal distribution family, regardless of the values of its parameters. A few other well-known distributions can be mesokurtic, depending on parameter values.
A distribution with positive excess kurtosis is called leptokurtic, or leptokurtotic. "Lepto-" means "slender."   In terms of shape, a leptokurtic distribution has fatter tails.  Examples of leptokurtic distributions include the Student’s t-distribution, Rayleigh distribution, Laplace distribution, exponential distribution, Poisson distribution and the logistic distribution.  Such distributions are sometimes termed super-Gaussian.
A distribution with negative excess kurtosis is called platykurtic, or platykurtotic. "Platy-" means "broad" In terms of shape, a platykurtic distribution has thinner tails. Examples of platykurtic distributions include the continuous and discrete uniform distribution, and the raised cosine distribution. The most platykurtic distribution of all is the Bernoulli distribution with p = 1/2 (for example the number of times one obtains "heads" when flipping a coin once, a coin toss), for which the excess kurtosis is −2. Suchdistributions are sometimes termed sub-Gaussian.
Table.1
Types of kurtosis and values
Sl.No.
Types of kurtosis
Values
1
Mesokurtic
0.263
2
Leptokurtic
<0.263
3
Platykurtic
>0.263


Applications of kurtosis. The sample kurtosis is a useful measure of whether there is a problem with outliers in a data set. Larger kurtosis indicates a more serious outlier problem, and may lead the researcher to choose alternative statistical methods.






POWER POINT ON KURTOSIS








Wednesday, October 24, 2018

MY PROFILE


Resume


Name                                      :           Vidhu Vijayan.c                                                     
Address                                   :           Cherchattil House
Cherpulassery
Palakkad (Dt)  Pin : 679 503
Father's Name                         :           Vijayan.K
Mother's Name                       :           Sushama.C
Age & Date of Birth                :          24,    24.03.1994
Religion                                   :          Hindu
Caste                                       :           Nair
Sex                                           :          Female
Marital Status                         :           Unmarried
Nationality                              :           Indian
Educational Qualification       :           BA History
:           B.Ed Social Science
Language Known                     :          English, Malayalam



DECLARATION

      I hereby declare that all the particulars furnished above are true to the best of my knowledge and belief.

Place : Cherpulassery                                                               
Date   :                                                                                                                       Signature