Calculate P(X(t)=x), the probability to make exactly x repeat transactions in
the interval (0, t]. This interval is in the estimation period and excludes values of t=0.
Note that here t is defined as the observation period T.cal which differs by customer.
# S4 method for clv.fitted.transactions
pmf(object, x = 0:5)The fitted transaction model.
Vector of positive integer numbers (>=0) indicating the number of repeat transactions x for which the PMF should be calculated.
Returns a data.table with ids and depending on x, multiple columns of PMF values, each column
for one value in x.
customer identification
PMF values for Y number of transactions
# \donttest{
data("cdnow")
# Fit the ParetoNBD model on the CDnow data
pnbd.cdnow <- pnbd(clvdata(cdnow, time.unit="w",
estimation.split=37,
date.format="ymd"))
#> Starting estimation...
#> Estimation finished!
# Calculate the PMF for 0 to 10 transactions
# in the estimation period
pmf(pnbd.cdnow, x=0:10)
#> Id pmf.x.0 pmf.x.1 pmf.x.2 pmf.x.3 pmf.x.4 pmf.x.5
#> 1: 1 0.6015503 0.1657156 0.08155493 0.04792002 0.03064000 0.02056505
#> 2: 10 0.6015503 0.1657156 0.08155493 0.04792002 0.03064000 0.02056505
#> 3: 100 0.6026941 0.1659529 0.08154711 0.04781471 0.03049773 0.02041476
#> 4: 1000 0.6134591 0.1679575 0.08125268 0.04665739 0.02905366 0.01894890
#> 5: 1001 0.6134591 0.1679575 0.08125268 0.04665739 0.02905366 0.01894890
#> ---
#> 2353: 995 0.6134591 0.1679575 0.08125268 0.04665739 0.02905366 0.01894890
#> 2354: 996 0.6134591 0.1679575 0.08125268 0.04665739 0.02905366 0.01894890
#> 2355: 997 0.6134591 0.1679575 0.08125268 0.04665739 0.02905366 0.01894890
#> 2356: 998 0.6134591 0.1679575 0.08125268 0.04665739 0.02905366 0.01894890
#> 2357: 999 0.6134591 0.1679575 0.08125268 0.04665739 0.02905366 0.01894890
#> pmf.x.6 pmf.x.7 pmf.x.8 pmf.x.9 pmf.x.10
#> 1: 0.01423779 0.010069592 0.007232370 0.005255241 0.003853191
#> 2: 0.01423779 0.010069592 0.007232370 0.005255241 0.003853191
#> 3: 0.01409371 0.009938364 0.007116532 0.005155115 0.003767935
#> 4: 0.01272869 0.008725213 0.006069147 0.004268411 0.003027769
#> 5: 0.01272869 0.008725213 0.006069147 0.004268411 0.003027769
#> ---
#> 2353: 0.01272869 0.008725213 0.006069147 0.004268411 0.003027769
#> 2354: 0.01272869 0.008725213 0.006069147 0.004268411 0.003027769
#> 2355: 0.01272869 0.008725213 0.006069147 0.004268411 0.003027769
#> 2356: 0.01272869 0.008725213 0.006069147 0.004268411 0.003027769
#> 2357: 0.01272869 0.008725213 0.006069147 0.004268411 0.003027769
# Compare vs. actuals (CBS in estimation period):
# x mean(pmf) actual percentage of x
# 0 0.616514 1432/2357= 0.6075519
# 1 0.168309 436/2357 = 0.1849809
# 2 0.080971 208/2357 = 0.0882478
# 3 0.046190 100/2357 = 0.0424268
# 4 0.028566 60/2357 = 0.0254561
# 5 0.018506 36/2357 = 0.0152737
# 6 0.012351 27/2357 = 0.0114552
# 7 0.008415 21/2357 = 0.0089096
# 8 0.005822 5/2357 = 0.0021213
# 9 0.004074 4/2357 = 0.0016971
# 10 0.002877 7/2357 = 0.0029699
# }