286 ◾ Simple Statistical Methods for Software Engineering
e plots have been made using the Excel function GAMMADIST. is func-
tion returns both the PDF and the Cumulative Distribution Function CDF.
e Excel syntax is defined as follows:
PDF(x) = GAMMA.DIST (x, shape parameter, scale parameter, 0)
CDF(x) = GAMMA.DIST (x, shape parameter, scale parameter, 1)
Box 18.1 Similarity Between Gamma and
loG-normal: makinG the ChoiCe
Gamma and log-normal distributions look alike.
Kundu and Manglick [1] compared gamma and log-normal distribution
and found them remarkably similar. ey have used Lawless [2] data of bear-
ing failure for this study. Let us develop some ideas around this analysis.
For Lawless data, we obtain gamma shape = 3.7138 and scale = 19.4489,
relating to Equation 18.1. Using Excel GAMMA.DIST (x, shape, scale, 0),
the gamma curve can be realized.
For the same data, we can obtain logarithms and find log-normal parame-
ters, mean of natural logarithms, and standard deviation of natural logarithms
of data. e log-normal curve can be realized by using Excel LOGNORM.
DIST (x, mean of Ln, standard deviation of Ln, o).
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 20 40 60 80 100
Shape = 1.2
Shape = 2
Shape = 3
1
β
α
Г(α)
x
α–1
e
β
–
Figure 18.1 Gamma distribution.