Bump version to 0.1.4

RELEASE_NOTES.md

@@ -1,6 +1,7 @@
 ### 0.1.4
 
 * Sampler state can be serialized to continue unfinished computation.
+* Fixed Mersenne twister copy constructor
 
 ### 0.1.3 - 2016-04-12
 

docs/content/tutorial.fsx

@@ -2,21 +2,63 @@
 // This block of code is omitted in the generated HTML documentation. Use 
 // it to define helpers that you do not want to show in the documentation.
 #I "../../bin/Angara.Statistics"
+#r "Angara.Statistics.dll"
 
 (**
-Introducing your project
-========================
 
-Say more
+### Distributions
+
+A `Distribution` is a value which allows to `draw` a pseudo-random number or compute a probability density function `log_pdf`.
+The `Distribution` discriminated union supports most common probability distributions like `Uniform` or `Normal`. More details are in a separate document page.
 
+For example, here is how you define normal distribution once you've referenced Angara.Statistics.dll:
 *)
-(*** define-output:sample ***)
-#r "Angara.Statistics.dll"
 open Angara.Statistics
 
 let distribution = Normal(37.0, 9.0)
+(**
+
+### Random number generator
+
+To draw random numbers we use [Mersenne Twister](http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html),
+one of the most commonly used random number generator.
+*)
 let generator = MT19937()
+let random_values =
+    generator.uniform_uint32(),  // low-level output
+    generator.uniform_float64(), // a floating point number from [0,1)
+    generator.normal()           // standard normal distribution with mean=0 and stdev=1
+(*** include-value:random_values ***)
+(**
+To reproduce the generator state use either exact seed or copy-constructor:
+*)
+let seed = generator.get_seed()
+let g' = MT19937(seed)
+let g'' = MT19937(generator)
+// the three instances should now produce
+// exactly the same sequence of pseudo-random numbers
+let test_3 = generator.normal(), g'.normal(), g''.normal()
+(*** include-value:test_3 ***)
+(**
+
+To draw a number from a non-standard distribution use `draw : MT19337 -> Distribution -> float`.
+For example, here we generate an array of 1000 random numbers from the above distribution.
+*)
 let samples = [| for _ in 1..1000 -> draw generator distribution |]
+(**
+
+### Probability density function
+
+One single function `log_pdf : Distribution -> float -> float` computes logarithm of normalized probability density
+of any distribution at any valid point.
+
+If you do not have a Distribution but have a sample from the distribution used kernel density estimator
+`kde : int -> float seq -> (float[] * float[])`. The estimator needs target number of points at which the density is to be evaluated.
+If this number is not a power of two he number of points will be the next larger power of two. The estimator returns two arrays of `x` and `y` values:
+
+The following sample code compares non-parametric density of the sample with the exact density from `log_pdf` function.
+*)
+(*** define-output:sample ***)
 // estimate density curve in 16 points
 let sampling_density_x, sampling_density_y = kde 16 samples
 // compute exact probability density function
@@ -30,5 +72,15 @@ Array.zip3 sampling_density_x sampling_density_y analytic_density_y
 (*** include-output:sample ***)
 
 (**
-Some more info
+
+### Sample statistics
+
+Use `summary` and `qsummary` functions to quickly compute mean, standard deviation, 95% and 68% quantiles of a sample:
 *)
+(*** define-output:summary ***)
+printfn "%A" (summary samples)
+(*** include-output:summary ***)
+(*** define-output:qsummary ***)
+printfn "%A" (qsummary samples)
+(*** include-output:qsummary ***)
+(** The `lb95` in the `qsummary` record stands for "lower bound of 95% interval" with is actually a 2.5% quantile. Similarly `ub95` stands for 97.5% quantile. *)