pmf {CLVTools}

Probability Mass Function

Description

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.

Usage

## S4 method for signature 'clv.fitted.transactions'
pmf(object, x = 0:5)

Arguments

object

The fitted transaction model.

x

Vector of positive integer numbers (>=0) indicating the number of repeat transactions x for which the PMF should be calculated.

Value

Returns a data.table with ids and depending on x, multiple columns of PMF values, each column for one value in x.

Id

customer identification

pmf.x.Y

PMF values for Y number of transactions

See Also

The model fitting functions pnbd, bgnbd, ggomnbd.

plot to visually compare the PMF values against actuals.

Examples

data("cdnow")

# Fit the ParetoNBD model on the CDnow data
pnbd.cdnow <- pnbd(clvdata(cdnow, time.unit="w",
                           estimation.split=37,
                           date.format="ymd"))

# Calculate the PMF for 0 to 10 transactions
#  in the estimation period
pmf(pnbd.cdnow, x=0:10)

# 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