# basss diffusion model

BASS扩散模型三个参数：＃最终购买产品的总人数，m; 创新系数p; 和＃系数的模仿，

q# exampleT79<-1:10Tdelt<-(1:100)/10Sales<-c(840,1470,2110,4000,7590,10950,10530,9470,7790,5890)Cusales<-cumsum(Sales)Bass.nls<-nls(Sales~M*(((P+Q)^2/P)*exp(-(P+Q)*T79))/(1+(Q/P)*exp(-(P+Q)*T79))^2,start=list(M=60630,P=0.03,Q=0.38))summary(Bass.nls)

##

## Formula: Sales ~ M * (((P + Q)^2/P) * exp(-(P + Q) * T79))/(1 + (Q/P) *

##    exp(-(P + Q) * T79))^2

##

## Parameters:

##  Estimate Std. Error t value Pr(>|t|)   

## M 6.80e+04  3.13e+03  21.74  1.1e-07 ***

## P 6.59e-03  1.43e-03    4.61  0.0025 **

## Q 6.38e-01  4.14e-02  15.41  1.2e-06 ***

## ---

## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##

## Residual standard error: 727 on 7 degrees of freedom

##

## Number of iterations to convergence: 8

## Achieved convergence tolerance: 7.32e-06

# get coefficient

Bcoef <- coef(Bass.nls)

m <- Bcoef[1]

p <- Bcoef[2]

q <- Bcoef[3]

＃将M的起始值设置为记录的总销售额。

ngete <- exp(-(p + q) * Tdelt)

# plot pdf

Bpdf <- m * ((p + q)^2/p) * ngete/(1 + (q/p) * ngete)^2

plot(Tdelt, Bpdf, xlab = "Year from 1979", ylab = "Sales per year", type = "l")

points(T79, Sales)

# plot cdfBcdf <- m * (1 - ngete)/(1 + (q/p) * ngete)plot(Tdelt, Bcdf, xlab = "Year from 1979", ylab = "Cumulative sales", type = "l")points(T79, Cusales)

＃当q = 0时，只有创新者没有模仿者。

Ipdf <- m * ((p + 0)^2/p) * exp(-(p + 0) * Tdelt)/(1 + (0/p) * exp(-(p + 0) *

    Tdelt))^2# plot(Tdelt, Ipdf, xlab = 'Year from 1979',ylab = 'Isales per year',# type='l')Impdf <- Bpdf - Ipdfplot(Tdelt, Bpdf, xlab = "Year from 1979", ylab = "Sales per year", type = "l",

    col = "red")lines(Tdelt, Impdf, col = "green")lines(Tdelt, Ipdf, col = "blue")

＃当q = 0时

Icdf <- m * (1 - exp(-(p + 0) * Tdelt))/(1 + (0/p) * exp(-(p + 0) * Tdelt))

# plot(Tdelt, Icdf, xlab = 'Year from 1979',ylab = 'ICumulative sales',

# type='l')

Imcdf <- m * (1 - ngete)/(1 + (q/p) * ngete) - Icdf

plot(Tdelt, Imcdf, xlab = "Year from 1979", ylab = "Cumulative sales", type = "l",

    col = "red")

lines(Tdelt, Bcdf, col = "green")

lines(Tdelt, Icdf, col = "blue")