season (version 0.2-6)

ciPhase: Mean and confidence interval for circular phase

Description

Calculates the mean and confidence interval for the phase based on a chain of MCMC samples.

Usage

ciPhase(theta, alpha = 0.05)

Arguments

theta

chain of Markov chain Monte Carlo (MCMC) samples of the phase.

alpha

the confidence level (default = 0.05 for a 95% confidence interval).

Value

• mean
  the estimated mean phase.
• lower
  the estimated lower limit of the confidence interval.
• upper
  the estimated upper limit of the confidence interval.

Details

The estimates of the phase are rotated to have a centre of $\pi$, the point on the circumference of a unit radius circle that is furthest from zero. The mean and confidence interval are calculated on the rotated values, then the estimates are rotated back.

References

Fisher, N. (1993) Statistical Analysis of Circular Data. Cambridge University Press. Page 36. Barnett, A.G., Dobson, A.J. (2010) Analysing Seasonal Health Data. Springer.

Examples

theta<-rnorm(n=2000,mean=0,sd=pi/50) # 2000 normal samples, centred on zero
hist(theta,breaks=seq(-pi/8,pi/8,pi/30))
ciPhase(theta)