algebraic.dist (version 0.9.1)

simplify.edist: Method for simplifying an edist object.

Description

Attempts to reduce expression distributions to closed-form distributions when mathematical identities apply. Supported rules include:

Usage

# S3 method for edist
simplify(x, ...)

Value

The simplified distribution, or unchanged edist if no rule applies

Arguments

x

The edist object to simplify

...

Additional arguments to pass (not used)

Details

Single-variable:

• c * Normal(mu, v) -> Normal(cmu, c^2v)

• c * Gamma(a, r) -> Gamma(a, r/c) for c > 0

• c * Exponential(r) -> Gamma(1, r/c) for c > 0

• c * Uniform(a, b) -> Uniform(min(ca,cb), max(ca,cb)) for c != 0

• c * Weibull(k, lam) -> Weibull(k, c*lam) for c > 0

• c * ChiSq(df) -> Gamma(df/2, 1/(2c)) for c > 0

• c * LogNormal(ml, sl) -> LogNormal(ml + log(c), sl) for c > 0

• Normal(mu, v) + c -> Normal(mu + c, v)

• Normal(mu, v) - c -> Normal(mu - c, v)

• Uniform(a, b) + c -> Uniform(a + c, b + c)

• Uniform(a, b) - c -> Uniform(a - c, b - c)

• Normal(0, 1) ^ 2 -> ChiSquared(1)

• exp(Normal(mu, v)) -> LogNormal(mu, sqrt(v))

• log(LogNormal(ml, sl)) -> Normal(ml, sl^2)

Two-variable:

• Normal + Normal -> Normal

• Normal - Normal -> Normal

• Gamma + Gamma (same rate) -> Gamma

• Exponential + Exponential (same rate) -> Gamma(2, rate)

• Gamma + Exponential (same rate) -> Gamma(a+1, rate)

• ChiSquared + ChiSquared -> ChiSquared

• Poisson + Poisson -> Poisson

• LogNormal * LogNormal -> LogNormal

Examples

# Normal + Normal simplifies to a Normal
z <- normal(0, 1) + normal(2, 3)
is_normal(z)  # TRUE
z             # Normal(mu = 2, var = 4)

# exp(Normal) simplifies to LogNormal
w <- exp(normal(0, 1))
is_lognormal(w)  # TRUE