#### Re: Freight car distribution

Mike Brock <brockm@...>

Larry Ostresh writes:

"I ran my "random train" Excel program for 100,000 iterations to test
whether it was working OK. The average number of boxcars per train,
by railroad, seemed to properly mirror the national fleet as
represented by Tim Gilbert's data for 1949:"

Larry, could you explain what you are talking about? You show RR [ i.e., SP excluding T&NO ], number [ number of SP box cars { 27757 } ] Nat'l % [ you show 4.0% but Tim shoed 3.9% ] and Random % [ 4.01% ]. What is the derivation of the random %?

RR___Number___Nat'l %___Random %

SP-Pac___27,757___4.00%___4.01%

"(The "Number" and "Nat'l %" columns above are from Tim's 1949 list of
boxcars."

Yep.

"His data are at "4060totalboxcarsUSownership.xls" in the
files section of this list."

Yep.

"The "Random %" column is the average
percentage of cars per train generated by my Excel program after
100,000 iterations. Each train consisted of 40 boxcars.)"

Hmmm. Well, 40 box cars is OK...actually 39.

"While running the program, I tallied the maximum number of cars for
each railroad over all the iterations. In a 40 boxcar train, the
average number of cars would be 40 times the national percentage
shown in the above table."

Why do you say that?

"For example, the average number of SP-Pac
cars would 40 * 4% = 1.6 cars - 1 or 2 cars per train."

Well...actually that's not so at all. The correct number is 4. 136/34= If you use real...rather than theoretical data. IOW, the 4% [ actually 3.9% ] fails to produce the actual number of cars...136.

"Any
particular 40 boxcar train may have more or less SP-Pac cars (0 to
40)."

"After 100,000 trials, there were in fact trains with no SP-Pac
boxcars, but no train had more than 9 of them."

We know that there were 4 of 34 trains...11.76%...of the trains with far more than 9 SP bx cars.

The 1953 data shows the "infamous" train with 36 or more SP bx cars [ not T&NO ].

Mike Brock

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