Define likelihoods using different different distribution families

likelihood(family, ...)

## Arguments

family

the likelihood distribution (see details)

...

see details

## Value

an object of class likelihood

## Details

### Available distribution families

The following distribution families can be used for the likelihood

• normal a normal distribution

• student_t a scaled and shifted t-distribution

• noncentral_t a noncentral t (for t statistic)

• noncentral_d a noncentral t (for one sample d)

• noncentral_d2 a noncentral t (for independent samples d)

• binomial a binomial distribution

The parameters that need to be specified will be dependent on the family

### normal distribution

When family is set to normal then the following parameters must be set

• mean mean of the normal likelihood

• sd standard deviation of the normal likelihood

### student_t distribution

When family is set to student_t then the following parameters may be set

• mean mean of the scaled and shifted t likelihood

• sd standard deviation of the scaled and shifted t likelihood

• df degrees of freedom

### noncentral_t distribution

When family is set to noncentral_t then the following parameters may be set

• t the t value of the data

• df degrees of freedom

### noncentral_d distribution

When family is set to noncentral_d then the following parameters may be set

• d the d (mean / sd) value of the data

• n the sample size

### noncentral_d2 distribution

When family is set to noncentral_d2 then the following parameters may be set

• d the d (mean / s_pooled) value of the data

• n1 the sample size of group 1

• n2 the sample size of group 2

$$s_{\mathrm{pooled}}$$ is set as below: $$s_{\mathrm{pooled}} = \sqrt{\frac{(n_1 - 1)s^2_1 + (n_2 - 1)s^2_2 } {n_1 + n_2 - 2}}$$

### binomial distribution

When the family is set to binomial then the following parameters may be set

• successes the number of successes

• trials the number of trials

## Examples

# specify a normal likelihood
likelihood(family = "normal", mean = 5.5, sd = 32.35)
#> Likelihood
#>   Family
#>     normal
#>   Parameters
#>     mean: 5.5
#>     sd: 32.35
#>

# specify a scaled and shifted t likelihood
likelihood(family = "student_t", mean = 5.5, sd = 32.35, df = 10)
#> Likelihood
#>   Family
#>     student_t
#>   Parameters
#>     mean: 5.5
#>     sd: 32.35
#>     df: 10
#>

# specify non-central t likelihood (t scaled)
likelihood(family = "noncentral_t", t = 10, df = 10)
#> Likelihood
#>   Family
#>     noncentral_t
#>   Parameters
#>     t: 10
#>     df: 10
#>

# specify non-central t likelihood (d scaled)
likelihood(family = "noncentral_d", d = 10, n = 10)
#> Likelihood
#>   Family
#>     noncentral_d
#>   Parameters
#>     d: 10
#>     n: 10
#>

# specify non-central t likelihood (independent samples d scaled)
likelihood(family = "noncentral_d2", d = 10, n1 = 10, n2 = 12)
#> Likelihood
#>   Family
#>     noncentral_d2
#>   Parameters
#>     d: 10
#>     n1: 10
#>     n2: 12
#>

# specify a binomial likelihood
likelihood(family = "binomial", successes = 2, trials = 10)
#> Likelihood
#>   Family
#>     binomial
#>   Parameters
#>     successes: 2
#>     trials: 10
#>