Description Usage Arguments Details Value Author(s) References See Also Examples
This function summarizes a 'dirichlet' object. It is a method for the
generic function summary
of class 'dirichlet'. It
calculate four types of theoretical summary statistics, which can be
compared with the corresponding observed statistics.
1 2 3 
object 
An object of "dirichlet" class. 
t 
Multiple of the base time period. For example, if the assumed
base time period is quarterly, then 
type 
A character vector that specifies which types of
theoretical statistics (during the time period indicated by

digits 
Number of decimal digits to control the rounding precision of the reported statistics. Default to 2. 
freq.cutoff 
For the 
heavy.limit 
For the 
dup.brand 
For the 
... 
Other parameters passing to the generic function. 
The output corresponds to the theoretical portion of the Table 3, 4, 5, 6 in the reference paper. We also have another set of functions (available upon request) that put observed and theoretical statistics together for making tables that resemble those in the reference.
Let P_n be the probability of a consumer buying the product category n times. Then P_n has a Negative Binomial Distribution (NBD). Let p(r_jn) be the probability of making r_j purchases of brand j, gien that n purchases of the category having been make (r_j≤q n). Then p(r_jn) has a BetaBinomial distribution.
The theoretical brand penetration b is then
b = 1  ∑_{n=0} P_n p(0n)
The theoretical brand buying rate w is
w = \frac{∑_{n=1} \{ P_n ∑_{r=1}^n r p(rn) \}}{b}
and the category buying rate per brand buyer w_P is
w_P = \frac{∑_{n=1} \{ n P_n [ 1  p(0n)] \}}{b}
The brand purchase frequency distribution is
f(r) = ∑_{n ≥q r} P_n p(rn)
The brand penetration given a specific category purchase frequency range R=\{i_1, i_2, i_3, …\} is
1  \frac{∑_{n \in R} P(n) p(0n)}{∑_{n \in R} P(n)}
The brand buying rate given a specific category purchase frequency range R=\{i_1, i_2, i_3, …\} is
\frac{∑_{n \in R} P(n) [∑_{r=1}^n r p(rn)]}{∑_{n \in R} P(n) [1  p(0n)] }
To calculate the brand duplication measure, we first get the penetration b_{(j+k)} of the "composite" brand of two brands j and k as:
b_{(j+k)} = 1  ∑_n P_n p_k(0n) p_j(0n)
Then the theoretical proportion b_{jk} of the population buying both brands at least once is:
b_{jk} = b_j + b_k  b_{(j+k)}
and the brand duplication b_{j/k} (where brand k is the focal brand) is:
b_{j/k} = b_{jk} / b_k
A list with those components that are specified by the input
type
parameter.
buy 
A data frame with three components: 
freq 
A matrix that lists the distribution of brand purchases. The number of rows is the number of brands. 
heavy 
A matrix with two columns. The first column
( 
dup 
A vector with dimension as the number of brands. It reports
the brand duplication (proportion of buyers of a particular brand
also buying other brand) of the focal brand ( 
Feiming Chen
The Dirichlet: A Comprehensive Model of Buying Behavior. G.J. Goodhardt, A.S.C. Ehrenberg, C. Chatfield. Journal of the Royal Statistical Society. Series A (General), Vol. 147, No. 5 (1984), pp. 621655
dirichlet
, print.dirichlet
,
plot.dirichlet
, NBDdirichletpackage
1 2 3 4 5 6 7 8 9 10 11 12 13  cat.pen < 0.56 # Category Penetration
cat.buyrate < 2.6 # Category Buyer's Average Purchase Rate in a given period.
brand.share < c(0.25, 0.19, 0.1, 0.1, 0.09, 0.08, 0.03, 0.02) # Brands' Market Share
brand.pen.obs < c(0.2,0.17,0.09,0.08,0.08,0.07,0.03,0.02) # Brand Penetration
brand.name < c("Colgate DC", "Macleans","Close Up","Signal","ultrabrite",
"Gibbs SR","Boots Priv. Label","Sainsbury Priv. Lab.")
dobj < dirichlet(cat.pen, cat.buyrate, brand.share, brand.pen.obs, brand.name)
## Not run: summary(dobj)
summary(dobj, t=4, type="freq")
summary(dobj, t=4, type="heavy", heavy.limit=c(7:50))
summary(dobj, t=1, type="dup", dup.brand=2)

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