Example 11.3

To conclude this module on the uses of stochastic processes in the area of marketing let us analyze the problem related to multibrand stochastic model where the aim is to describe the occurrence over time of purchases of the product class and a multibrand stochastic choice model which specifies how a brand may be chosen on a given purchase occasion.

Before describing the model let us go through the variable/statistics which are important for a better understanding of the model, and they are:

1. Market share: Proportion of the sales of the product class that corresponds to a specific brand  during the  period of the analysis, and it is denoted by .
   
   
2. Market penetration: Proportion of the population who buy brand  at least once during a given interval of time, and it may be denoted by , where  is the time period.
   
   
3. Duplication: Proportion of the population who buy both brands  and  at least once during the interval considered, and it is denoted by .
   
   
4. Brand switching: Denotes the proportion of purchase occasion such that a different brand is bought during the next purchase occasion. Thus it refers to the concept of switching from brand  to brand , and is denoted by .
   
   
5. Conditional switching: It denotes the proportion of purchase occasion such that a different brand is bought on the next purchase occasion. Here one important fact to be remembered is that the second purchase is definitely dependent on the first. As in the previous case this also refers to the concept of switching from brand  to brand , but is now denoted by .
   
   
6. Repeat buying: Denotes the time that any brand is bought on two consecutive occasions. Repeat buying can also be applied to one specific brand and is given by the formulae  or  depending on the background of how the repeat purchases or buying are being done. One should remember that RB=1-TS, where RB means repeat buying while TS is total switching.