生物统计学第三次作业

#1. 二项分布

plot(NULL, xlim=c(0, 20), ylim=c(0, 0.25), xlab='X', ylab='p', main='Binomial Distribution')
for(p in seq(0.1, 0.9, by=0.2)){
  binom.d = dbinom(seq(0, 20), size=20, prob=p)
  lines(binom.d, type='l', col=rainbow(5)[which(seq(0.1, 0.9, by=0.2)==p)])
  legend(10, 0.25 - (p*0.2), paste('p =', p), text.col=rainbow(5)[which(seq(0.1, 0.9, by=0.2)==p)], box.lty=0, cex=0.8)
}

2. 泊松分布

lambda = 1
poisson.d= dpois(seq(1,20), lambda)
plot(poisson.d, xlab= 'X', ylab='p', type='l', ylim=c(0, 0.4), main='Poisson Distribution')
for(lambda in 1:10){
  poisson.d= dpois(seq(1,20), lambda)
  lines(poisson.d, type= 'l', col= rainbow(10)[lambda])
  legend(lambda, 0.4-lambda/50, paste('lambda =', lambda, sep=' '), text.col= rainbow(10)[lambda], box.lty= 0, cex= 0.5)
}

3. 负二项分布

plot(NULL, xlim=c(0, 30), ylim=c(0, 0.25), xlab='X', ylab='p', main='Negative Binomial Distribution')
for(p in seq(0.2, 1.0, by=0.2)){
  nbinom.d = dnbinom(seq(0, 30), size=5, prob=p)
  lines(nbinom.d, type='l', col=rainbow(5)[which(seq(0.2, 1.0, by=0.2)==p)])
  legend(15, 0.25 - (p*0.2), paste('prob =', round(p, 1)), text.col=rainbow(5)[which(seq(0.2, 1.0, by=0.2)==p)], box.lty=0, cex=0.8)
}

4.正态分布

x_seq = seq(-4, 4, length=100)
plot(NULL, xlim=c(-4, 4), ylim=c(0, 1.0), xlab='X', ylab='p', main='Normal Distribution')
for(sd_val in seq(0.5, 2.5, by=0.5)){
  normal.d = dnorm(x_seq, mean=0, sd=sd_val)
  lines(x_seq, normal.d, type='l', col=rainbow(5)[which(seq(0.5, 2.5, by=0.5)==sd_val)])
  legend(sd_val, 1.0 - (sd_val*0.15), paste('sd =', sd_val), text.col=rainbow(5)[which(seq(0.5, 2.5, by=0.5)==sd_val)], box.lty=0, cex=0.8)
}

5.幂律分布

x_seq = seq(1, 20, length=100)
plot(NULL, xlim=c(1, 20), ylim=c(0, 1.0), xlab='X', ylab='p', main='Power Law Distribution')
for(alpha in seq(1, 5, by=1)){
 
  power.d = x_seq^(-alpha)
 
  power.d = power.d / sum(power.d) * 5 
  
  lines(x_seq, power.d, type='l', col=rainbow(5)[which(seq(1, 5, by=1)==alpha)])
  legend(alpha, 1.0 - (alpha*0.15), paste('alpha =', alpha), text.col=rainbow(5)[which(seq(1, 5, by=1)==alpha)], box.lty=0, cex=0.8)
}