HSROC (version 2.1.9)

beta.parameter: A function that returns the shape parameters of the beta distribution

Description

When provided the minimum and maximum values corresponding to the prior information on a parameter (within [0, 1]), the function returns the shape parameters of the beta distribution, namely \(\alpha\) and \(\beta\), that covers this range.

Usage

beta.parameter(low, up)

Arguments

low

numeric argument. Lower bound of the range

up

numeric argument. Upper bound of the range

Value

It returns a list object consisting of the shape parameters alpha and beta of the Beta distribution such that $$\frac{\alpha}{\alpha + \beta} = \frac{low + up}{2}$$ and $$\frac{\alpha \beta}{(\alpha + \beta)^2(\alpha + \beta + 1)} = \frac{up - low}{4}$$

The function has been built such that the particular case where \(low = up = 1\) will return \(\alpha = \beta = 1\).

Details

The low argument must always be less than the up argument. Also, both low and up arguments must remain within [0, 1].

Examples

# NOT RUN {
  

# }
# NOT RUN {
beta.parameter(-1, 0.5)
# }
# NOT RUN {
 #Returns error!
# }
# NOT RUN {
beta.parameter(0, 0)
# }
# NOT RUN {
 #Not allowed.  Returns error!
# }
# NOT RUN {
beta.parameter(0.75, 0.25)
# }
# NOT RUN {
 #Returns error!

beta.parameter(0, 1)
beta.parameter(0.5, 1) 
beta.parameter(0.1, 0.7)            

# }