Coeficiente de CURTOSE: para que serve e como calculá-lo? Noções de Estatística #10

Kurtosis describes the degree of flatness of a distribution. We will see below how to define kurtosis measures for the observed data My name is Alexandre Patriota, I am a professor of statistics, in this video I am going to talk about how the kurtosis of the observed data can help us in describing the data distribution. Like asymmetry, kurtosis offers important information about the form of data distribution. More specifically, it measures the decay of the tails of the distribution in relation to a central position measure that can be the mean or the median. To facilitate the discussion, I will consider only data whose frequency density is symmetrical, and is concentrated around the average. In this case, the frequency density of the data reaches its maximum point in values ​​around the median or average. In addition, the frequency density decreases as the point moves away from the central position. If this decay is slow, we say that the distribution has heavy tails, that is, the tail persists in having relatively high density. If the decay is rapid or abrupt, we say that the distribution has light tails, that is, the tail of the distribution has low density. Pearson defined the kurtosis coefficient as the fourth central moment divided by the standard deviation to the fourth power. The fourth central moment is given by the average of the differences between the average and the observations raised to the fourth power, the kurtosis coefficient is obtained by dividing the fourth central moment by the standard deviation raised to the fourth power. Assignments: ARROW Icons made by Pixel perfect https://www.flaticon.com/authors/pixe... 00:00 INTRODUCTION 02:03 CURTOSIS COEFFICIENT 02:25 INTERPRETATION OF MOORS 1986 02:45 THEORETICAL BACKGROUND 03:12 STANDARD OBSERVATIONS 04:42 VARIANCE OF STANDARDIZED VARIABLES TO THE SQUARE 05:35 COEFFICIENT OF CURTOSIS FOR TWO OBSERVATIONS 06:13 CALCULATING THE CURTOSIS 07:25 DATA WITH LEPTOCHURTIC DISTRIBUTION 08:15 TAIL COMPARISON 08:25 DATA WITH PLATICULTURAL DISTRIBUTION 09:12 FINAL DISCUSSION 09:53 RECORDING ERRORS