adopters
first-time purchasers of a product or first-time users of an innovation. See
adoptions.
adoptions
First-time purchases of a product or first-time uses of an innovation In the
Bass Model the number of adoptions is equal to the number of adopters, therefore
these terms are used interchangeably. See adopters.
Bass Model differential equation (DE)
Since the left side is f(t), the DE equation is also
Expressed in terms of adoptions
where a(t) is adoptions at time t and A(t) is cumulative adoptions at time
t.
See Which Bass
Model Equation Should I Use?
Bass Model differential equation solution
See Which Bass
Model Equation Should I Use?
Bass Model discrete forms
A discrete form of the Bass Model is required for the real world because
adoptions (sales to first time buyers) are measured in discrete time intervals (e.g.,
years).
See Which Bass
Model Equation Should I Use?
Bass Model discrete form - F(t)-based form (Srinivasan
Mason form)
In this form, f(t) is expressed in terms of F(t) as
.
See Which Bass
Model Equation Should I Use?
Bass Model discrete form - f(t)-based
form
See Which Bass
Model Equation Should I Use?
Bass Model principle
See Bass Model Home Page
category
See product category
discrete time
In discrete time, time (usually denoted t) can only take specific values such as 1, 2 3, ... or 1.5, 2.5,
3.5, ... or -9.2, -7.3, -4.1 and other specific values. Discrete time does
not mean that time can take only integer values (e..g, 1, 2, 3, ....) but
integer values are normally the case in the Bass Model.
F
The Bass cumulative probability distribution (CDF).
The probability that a potential adopter will have adopted the product
at t.
Also, the portion of the potential market that
will have adopted at time t.
In continuous form,
.
This can be simplified using
to obtain
and further simplified using
to get
.
f(t)
The Bass probability distribution (PDF).
The probability that a potential adopter will adopt the product at time t
given that they have not yet adopted.
also, the portion of the potential market that
adopts at time t.
In continuous form,
.
This can be simplified by using
to obtain
and further simplified using
to
which rearranges to
.
M
Bass Model parameter M represents the potential market size, which is the
maximum number of adopters that will ever adopt the product
p
Bass Model parameter p
peak in adoptions
to do
penetration
to do
product
Used interchangeably with product category.
to do
product category
to do
q
Bass Model parameter q