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Kurtosis: The extent to which the peak of the unimodal probability distribution or the frequency distribution departs from its shape of the normal distribution, by either being more pointed (like leptokurtic)or flatter ( like platykurtic). Commonly measured for a probability distribution as
where 4 is the fourth central moment of distribution, and 2 is its variance.
(consequent functions of sample moments are used for frequency distributions.)
For the normal distribution this index takes the value three and often index is redefined as the value above minus three so that the normal distribution would contain the value zero.
(Other distributions with the zero kurtosis are known as mesokurtic.) For the distribution which is leptokurtic the index is positive and for the platykurtic curves it is negative. It is shown in the figure
Minimum volume ellipsoid is a term for ellipsoid of the minimum volume which covers some specified proportion of the set of multivariate data. It is commonly used to construct rob
O. J. Simpson paradox is a term coming from the claim made by the defence lawyer in murder trial of O. J. Simpson. The lawyer acknowledged that the statistics demonstrate that onl
Principal components analysis is a process for analysing multivariate data which transforms original variables into the new ones which are uncorrelated and account for decreasing
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A term usually used for unobserved individual heterogeneity. Such variation is of main concern in the medical statistics particularly in the analysis of the survival times where ha
how to find the PDF and CDF of a gamma random variable with given equation?
(a) A plane timetable states that a particular plane is due at 2pm but the actual arrival time isuniformly distributed between 1pm and 3pm. (i) Calculate the probability that th
A directed graph is simple if each ordered pair of vertices is the head and tail of at most one edge; one loop may be present at each vertex. For each n ≥ 1, prove or disprove the
Remedian: The robust estimator of location which is computed by an iterative process. By assuming that the sample size n can be written as bk where b and k are the integers, the s
Contour plot : A topographical map drawn from data comprising observations on the three variables. One variable is represented on horizontal axis and the second variable is represe
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