Fix some docstrings (#1404)

* fix docstrings

* clean up Chernoff

src/univariate/continuous/beta.jl

@@ -1,5 +1,5 @@
 """
-    Beta(α,β)
+    Beta(α, β)
 
 The *Beta distribution* has probability density function
 
@@ -15,10 +15,10 @@ independently, then ``X / (X + Y) \\sim \\operatorname{Beta}(\\alpha, \\beta)``.
 
 ```julia
 Beta()        # equivalent to Beta(1, 1)
-Beta(a)       # equivalent to Beta(a, a)
-Beta(a, b)    # Beta distribution with shape parameters a and b
+Beta(α)       # equivalent to Beta(α, α)
+Beta(α, β)    # Beta distribution with shape parameters α and β
 
-params(d)     # Get the parameters, i.e. (a, b)
+params(d)     # Get the parameters, i.e. (α, β)
 ```
 
 External links

src/univariate/continuous/betaprime.jl

@@ -1,5 +1,5 @@
 """
-    BetaPrime(α,β)
+    BetaPrime(α, β)
 
 The *Beta prime distribution* has probability density function
 
@@ -15,10 +15,10 @@ relation ship that if ``X \\sim \\operatorname{Beta}(\\alpha, \\beta)`` then ``\
 
 ```julia
 BetaPrime()        # equivalent to BetaPrime(1, 1)
-BetaPrime(a)       # equivalent to BetaPrime(a, a)
-BetaPrime(a, b)    # Beta prime distribution with shape parameters a and b
+BetaPrime(α)       # equivalent to BetaPrime(α, α)
+BetaPrime(α, β)    # Beta prime distribution with shape parameters α and β
 
-params(d)          # Get the parameters, i.e. (a, b)
+params(d)          # Get the parameters, i.e. (α, β)
 ```
 
 External links

src/univariate/continuous/cauchy.jl

@@ -9,12 +9,12 @@ f(x; \\mu, \\sigma) = \\frac{1}{\\pi \\sigma \\left(1 + \\left(\\frac{x - \\mu}{
 
 ```julia
 Cauchy()         # Standard Cauchy distribution, i.e. Cauchy(0, 1)
-Cauchy(u)        # Cauchy distribution with location u and unit scale, i.e. Cauchy(u, 1)
-Cauchy(u, b)     # Cauchy distribution with location u and scale b
+Cauchy(μ)        # Cauchy distribution with location μ and unit scale, i.e. Cauchy(μ, 1)
+Cauchy(μ, σ)     # Cauchy distribution with location μ and scale σ
 
-params(d)        # Get the parameters, i.e. (u, b)
-location(d)      # Get the location parameter, i.e. u
-scale(d)         # Get the scale parameter, i.e. b
+params(d)        # Get the parameters, i.e. (μ, σ)
+location(d)      # Get the location parameter, i.e. μ
+scale(d)         # Get the scale parameter, i.e. σ
 ```
 
 External links

src/univariate/continuous/chernoff.jl

@@ -16,7 +16,7 @@ The *Chernoff distribution* is the distribution of the random variable
 ```math
 \\underset{t \\in (-\\infty,\\infty)}{\\arg\\max} ( G(t) - t^2 ),
 ```
-where ``G`` is standard two--sided Brownian motion.
+where ``G`` is standard two-sided Brownian motion.
 
 The distribution arises as the limit distribution of various cube-root-n consistent estimators,
 including the isotonic regression estimator of Brunk, the isotonic density estimator of Grenander,
@@ -27,21 +27,7 @@ computation of pdf and cdf is based on the algorithm described in Groeneboom and
 Journal of Computational and Graphical Statistics, 2001.
 
 ```julia
-Chernoff()
-pdf(Chernoff(),x::Real)
-cdf(Chernoff(),x::Real)
-logpdf(Chernoff(),x::Real)
-survivor(Chernoff(),x::Real)
-mean(Chernoff())
-var(Chernoff())
-skewness(Chernoff())
-kurtosis(Chernoff())
-kurtosis(Chernoff(), excess::Bool)
-mode(Chernoff())
-entropy(Chernoff())
-rand(Chernoff())
-rand(rng, Chernoff()
-cdf(Chernoff(),-x)              #For tail probabilities, use this instead of 1-cdf(Chernoff(),x)
+cdf(Chernoff(),-x)              # For tail probabilities, use this instead of 1-cdf(Chernoff(),x)
 ```
 """
 struct Chernoff <: ContinuousUnivariateDistribution

src/univariate/continuous/symtriangular.jl

@@ -1,5 +1,5 @@
 """
-    SymTriangularDist(μ,σ)
+    SymTriangularDist(μ, σ)
 
 The *Symmetric triangular distribution* with location `μ` and scale `σ` has probability density function
 
@@ -9,8 +9,8 @@ f(x; \\mu, \\sigma) = \\frac{1}{\\sigma} \\left( 1 - \\left| \\frac{x - \\mu}{\\
 
 ```julia
 SymTriangularDist()         # Symmetric triangular distribution with zero location and unit scale
-SymTriangularDist(u)        # Symmetric triangular distribution with location μ and unit scale
-SymTriangularDist(u, s)     # Symmetric triangular distribution with location μ and scale σ
+SymTriangularDist(μ)        # Symmetric triangular distribution with location μ and unit scale
+SymTriangularDist(μ, s)     # Symmetric triangular distribution with location μ and scale σ
 
 params(d)       # Get the parameters, i.e. (μ, σ)
 location(d)     # Get the location parameter, i.e. μ