A report is given to supplement the progress report of June 17, 1977. In that progress report gamma, lognormal, and Rayleigh probability density functions were fitted to the times between lightning flashes in the storms of 9/12/75, 8/26/75, and 7/13/76 by the maximum likelihood method. The goodness of fit is checked by the Kolmogoroff-Smirnoff test. Plots of the estimated densities along with normalized histograms are included to provide a visual check on the goodness of fit. The lognormal densities are the most peaked and have the highest tails. This results in the best fit to the normalized histogram in most cases. The Rayleigh densities have too broad and rounded peaks to give good fits. In addition, they have the lowest tails. The gamma densities fall inbetween and give the best fit in a few cases

Tretter, S. A.

English

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https://ntrs.nasa.gov/search.jsp?R=19770021720 2020-03-22T07:58:47+00:00Z
iEstimated Probability Density Functions for the
Times Bet ,.veen Flashes in the Storms of
9/ 12/75, 8/26/75, and 7/13/76
by
S. A. Trette r
Co-Principal Investigator
Prepared for NASA Grant NSG 5048
LS11.,-;A1ED VFQBABILITY	 N77-28664
9S FOR THE TIMES BET'iEEN
;TORMS CF 12 SEPTEMBER 1975,
ANL 13 JULY 1976 (Maryland	 Uuclas
AC3/MF A01	 CSCI 04A G3/4b 3928y
August 17, 1977
'ARTMENT OF
CAL ENGINEERING
RSITY OF MARYLAND
EGE PARK, MARYLAND 20742 i
A UG 7977 ^ 1
RTEIVED
	
=^
NASA STI FACILITY
INPUT BRANCH
V--_
Estimated Probability Density Functions for the
Times Between Flashes in the Storms of
9/12/75, 8/26/75, and 7/13/76
i
i
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i
i
i
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ll
u
u
by
S. A. Tretter
Co- Principal Investigator
Prepared for NASA Grant NSG 5048
August 17, 1977
Department of Electrical Engineering
University of Maryland
College Park, Maryland 20742
0
List of Figures
{
s
Fig. l Storm of 9/ 12/75 (Tape 1) - Estimated Densities 2
Fig. 2 Storm of 9/12/75 (Tape 1) - Normalized Histogram 3
Fig. 3 Storm of 9/ 12/75 (Tape 2) - Estimated Densities 4
Fig. 4 Storm of 9/12/75 (Ta pe 2) - Normalized Histogram 5
Fig. 5 Storm of 9/12/75 (Tape 3) - Estimated Densities 6	 1
Fig. 6 Storm of 9/!2/75 (Tape 3) - Normalized Histogram 7
Fig. 7 Storm of 9/12/75 (Tape 4) - Estimated Densities 8
Fig. 8 Storm of 9/12/75 (Tape 4) - Normalized Histogram 9	 a
Fig. 9 Storm of 9/12/75 (Tape 5) - Estimated Densities 10
Fig. 10 Storm of 9/12/75 (Tape 5) - Normalized Histogram 1	 1
Fig. 11 Storm of 8/26/75 (Tape 1) - Estimated Densities 12
Fig. 12 Storm of 8/26/75 (Tape 1) - Normalized Histogram 13
Fig. 13 Storm of 8/26/75 (Tape 2) - Estimated Densities 14
Fig. 14 Storm of 8/26/75 (Tape 2) - Normalized Histogram 15
Fig. 15 Storm of 8/26/75 (Tape 3) - Estimated Densities 16
Fig. 16 Storm of 8/26/75 (Tape 3) - Normalized Histogram 17
Fig. 17 Storm of 8/26/75 (Tape 4) - Estimated Densities 18
Fig. 18 Storm of 8/26/75 (Tape 4) - Normalized Histogram 19
Fig. 19 Storm of 7/13/76 (Tape 1) - Estimated Densities
(All Flashes) 20
Fig. 20 Storm of 7/13/76 (Tape 1) - Normalized Histogram
(All Flashes) 21
Fig. 21 Storm of 7/ 13/76 (Tape 2) - Estimated Densities
(All Flashes) 22
i
E
Fig. 22
	
Storm of 7/ 13/76 (Tape 2) - Normalized Histogram
(All Flashes) 23
Fig. 23 Storms of 7/ 13/76 (Tape 3) - Estimated Densities
(All Flashes) 24
Fig. 24 Storm of 7/ 13/76 (Tape 3) - Normalized Histogram
(All Flashes) 25
Fig. 25 Storm of 7/13/76 (Tape 1) - Estimated Densities
(Cloud to Ground Flashes) 26
Fig. 26 Storm of 7/ 13/76 (Tape 1) - Normalized Histogram
(Cloud to Ground Flashes) 27
Fig. 27 Storm of 7/13/76 (Tape 2) - Estimated Densities
(Cloud to Ground Flashes) 28
Fig. 28 Storm of 7/13/76 (Tape 2) - Normalized Histogram
(Cloud to Ground Flashes) 29
Fig. 29 Storm of 7/ 13/76 (Tape 3) - Estimated Densities
(Cloud to Ground Flashes) 30
Fig. 30 Storm of 7/13/76 (Tape 3) - Normalized Histogram
( Cloud to Ground Flashes) 31
..
AEstimated Probability Density Functions for the
Times Between Flashes in the Storms of
9/12/75, 8/26/75, and 7/13/76
This report supplements the progress report of June 17, 1977. In
..	 that progress report gamma, lognormal, and Rayleigh probability density
functions were fitted to the times between lightning flashes in the storms of
9/12/75, 8/26/75, and 7/13/76 by the maximum likelihood method. The
igoodness of fit was checked by the Kolmogorov-Smirnov test. Plots of
11	
the estimated densities along with normalized histograms are included
in this report to provide a visual check on the goodness of fit. The labels
on the top right hand sides of the graphs refer to the tables in the progress
report.
From the figures it can be seen that the lognormal densities are
the most peaked and have the highest tails. This results in the best fit to
the normalized histogram in most cases. The Rayleigh densities have too
broad and rounded peaks to give good fits. In addition, they have the
lowest tails. Tha gamma densities fall inbetween and give the best fit
in a few cases.
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Estimated probability density functions for the times between flashes in the storms of 12 September 1975, 26 August 1975, and 13 July 1976

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