BinomialTreeOption
> CRRTree = BinomialTreeOption(TypeFlag = "pa", S = 50, X = 50,+ Time = 0.4167, r = 0.1, b = 0.1, sigma = 0.4, n = 5)
> BinomialTreePlot(CRRTree, dy = 1, cex = 0.8, ylim = c(-6, 7),
+ xlab = "n", ylab = "Option Value")
> title(main = "Option Tree")
binom.test(c(682, 243), p = 3/4)
Exact binomial test
data: c(682, 243)
number of successes = 682, number of
trials = 925, p-value = 0.3825
alternative hypothesis: true probability of success is not equal to 0.75
95 percent confidence interval:
0.7076683 0.7654066
sample estimates:
probability of success
0.7372973
Quasi test
> binom.test(682, 682 + 243, p = 3/4)
Exact binomial test
data: 682 and 682 + 243
number of successes = 682, number of
trials = 925, p-value = 0.3825
alternative hypothesis: true probability of success is not equal to 0.75
95 percent confidence interval:
0.7076683 0.7654066
sample estimates:
probability of success
0.7372973
> x <- rnorm(100)
> y <- rpois(100, exp(1+x))
> glm(y ~ x, family = quasi(variance = "mu", link = "log"))
Call: glm(formula = y ~ x, family = quasi(variance = "mu", link = "log"))
Coefficients:
(Intercept) x
1.0435 0.9478
Degrees of Freedom: 99 Total (i.e. Null); 98 Residual
Null Deviance: 487.7
Residual Deviance: 117 AIC: NA
> glm(y ~ x, family = poisson)
Call: glm(formula = y ~ x, family = poisson)
Coefficients:
(Intercept) x
1.0435 0.9478
Degrees of Freedom: 99 Total (i.e. Null); 98 Residual
Null Deviance: 487.7
Residual Deviance: 117 AIC: 389.7
> glm(y ~ x, family = quasi(variance = "mu^2", link = "log"))
Call: glm(formula = y ~ x, family = quasi(variance = "mu^2", link = "log"))
Coefficients:
(Intercept) x
1.0777 0.8539
Degrees of Freedom: 99 Total (i.e. Null); 98 Residual
Null Deviance: 87.08
Residual Deviance: 26.21 AIC: NA
> y <- rbinom(100, 1, plogis(x))
> glm(y ~ x, family = quasi(variance = "mu(1-mu)", link = "logit"), start = c(0,1))
Call: glm(formula = y ~ x, family = quasi(variance = "mu(1-mu)", link = "logit"),
start = c(0, 1))
Coefficients:
(Intercept) x
-0.5203 1.0420
Degrees of Freedom: 99 Total (i.e. Null); 98 Residual
Null Deviance: 134.6
Residual Deviance: 114.2 AIC: NA
> bi <- binomial()
> et <- seq(-10,10, by=1/8)
> plot(et, bi$mu.eta(et), type="l")
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