1 WHY WE USE EXPLORATORY DATA ANALYSIS DATA YES NO ESTIMATES BASED ON NORMAL DISTRIB. KURTOSIS, SKEWNESS TRANSFORMATIONS QUANTILE (ROBUST) ESTIMATES OUTLIERS.

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Presentation transcript:

1 WHY WE USE EXPLORATORY DATA ANALYSIS DATA YES NO ESTIMATES BASED ON NORMAL DISTRIB. KURTOSIS, SKEWNESS TRANSFORMATIONS QUANTILE (ROBUST) ESTIMATES OUTLIERS EXTREMS YES NO QUANTILE (ROBUST) ESTIMATES WHY ? CAN WE REMOVED THEM ? DO DATA COME FROM NORMAL DISTRIBUTION? TRANSFORMATIONS

2 METHODS OF EDA Graphical: dot plot box plot notched box plot QQ plot histogram density plots Tests: tests of normality minimal sample size

3 DOT PLOT

4 BOX PLOT lower quartil upper kvartil fence outer inner fence inner outer interquartile range (H) číselná osa median

5 NOTCHED BOX PLOT interval estimate of median RFRF

6 Q-Q PLOT X: theoretical quantiles of analysed distribution Y: sample quantiles ideal coincidence of sample values and theoretical distribution measured values

7 Q-Q GRAF

8

9 Q-Q plot right sided – skewed to left left sided – skewed to right platycurtic („flat“) leptocurtic(„steep“)

10

11

12 HISTOGRAM

13 HISTOGRAM correct width of interval:

14 HISTOGRAM – kernel density function

15 TRANSFORMATION Aim of transformation: reduction of variance better level of symmetry(normality) of data Transformation function: non-linear function monotonic function

16 TRANSFORMATION – basic concept

17 TRANSFORMATION – logaritmic transformation

18 TRANSFORMATION – power transformation

19 TRANSFORMATION – Box-Cox

20 TRANSFORMATION – Box-Cox

21 TRANSFORMATION– estimate of optimal logarithm of likelihood function for various values of optimal interval estimate of parameter = 1 is not included in interval estimate of. It means that transformation will be probably successful 1.00 maxLF– 0,5* quantile  2