Improve docs

README.md

@@ -5,52 +5,14 @@
 [![codecov](https://codecov.io/gh/JuliaDynamics/StreamSampling.jl/graph/badge.svg?token=F8W0MC53Z0)](https://codecov.io/gh/JuliaDynamics/StreamSampling.jl)
 [![Aqua QA](https://raw.githubusercontent.com/JuliaTesting/Aqua.jl/master/badge.svg)](https://github.com/JuliaTesting/Aqua.jl)
 
+The scope of this package is to provide general methods to sample from any stream in a single pass through the data, even when 
+the number of items contained in the stream is unknown.
 
-This package allows to sample from any stream in a single pass through the data, 
-even if the number of items is unknown. 
-
-If the iterable is lazy, the memory required grows in relation to the size of the 
-sample, instead of the all population, which can be useful for sampling from big 
-data streams.
-
-Moreover, it turns out that sampling with the techniques implemented in this library
-is also much faster in some common cases, as highlighted below:
-
-
-```julia
-julia> using StreamSampling
-
-julia> using BenchmarkTools, Random, StatsBase
-
-julia> rng = Xoshiro(42);
-
-julia> iter = Iterators.filter(x -> x != 10, 1:10^7);
-
-julia> wv(el) = 1.0
-
-julia> @btime itsample($rng, $iter, 10^4, algRSWRSKIP);
-  11.744 ms (5 allocations: 156.39 KiB)
-
-julia> @btime sample($rng, collect($iter), 10^4; replace=true);
-  131.933 ms (20 allocations: 146.91 MiB)
-
-julia> @btime itsample($rng, $iter, 10^4, algL);
-  10.260 ms (3 allocations: 78.22 KiB)
-
-julia> @btime sample($rng, collect($iter), 10^4; replace=false);
-  132.069 ms (27 allocations: 147.05 MiB)
-
-julia> @btime itsample($rng, $iter, $wv, 10^4, algWRSWRSKIP);
-  32.278 ms (18 allocations: 547.34 KiB)
-
-julia> @btime sample($rng, collect($iter), Weights($wv.($iter)), 10^4; replace=true);
-  348.220 ms (49 allocations: 675.21 MiB)
-
-julia> @btime itsample($rng, $iter, $wv, 10^4, algAExpJ);
-  39.965 ms (11 allocations: 234.78 KiB)
-
-julia> @btime sample($rng, collect($iter), Weights($wv.($iter)), 10^4; replace=false);
-  306.039 ms (43 allocations: 370.19 MiB)
-```
+This has some advantages over other sampling procedures:
 
+- If the iterable is lazy, the memory required grows in relation to the size of the sample, instead of the all population.
+- The sample collected is a random sample of the portion of the stream seen thus far at any point of the sampling process.
+- In some cases, sampling with the techniques implemented in this library can bring considerable performance gains, since
+  the population of items doesn't need to be previously stored in memory.
+
 More information can be found in the [documentation](https://juliadynamics.github.io/StreamSampling.jl/dev/).

docs/src/index.md

@@ -1,18 +1,23 @@
 
-# Introduction
+## Introduction
 
-This package allows to sample from any stream in a single pass through the data, even if the number of items is unknown.
+The scope of this package is providing general methods to sample from any stream in a single pass through the data, even when the number of items contained in the stream is unknown.
 
-If the iterable is lazy, the memory required grows in relation to the size of the sample, instead of the all population, which can be useful for sampling from big data streams.
+This has some advantages over other sampling procedures:
 
-# Example Usage
+- If the iterable is lazy, the memory required grows in relation to the size of the sample, instead of the all population.
+- The sample collected is a random sample of the portion of the stream seen thus far at any point of the sampling process.
+- In some cases, sampling with the techniques implemented in this library can bring considerable performance gains, since
+  the population of items doesn't need to be previously stored in memory.
 
-The [`itsample`](@ref) instead allows to consume all the stream at once and return the sample collected:
+## Brief overview of the functionalities
+
+The [`itsample`](@ref) function allows to consume all the stream at once and return the sample collected:
 
 ```julia
 julia> using StreamSampling
 
-julia> st = 1:10;
+julia> st = 1:100;
 
 julia> itsample(st, 5)
 5-element Vector{Int64}:
@@ -43,4 +48,48 @@ julia> value(rs)
  74
 ```
 
-Consult the [API page](https://juliadynamics.github.io/StreamSampling.jl/stable/api/) for more information on the available functionalities.
+Consult the [API page](https://juliadynamics.github.io/StreamSampling.jl/stable/api/) for more information on these and other functionalities.
+
+## Benchmark
+
+As stated in the first section, using these sampling techniques can bring down considerably the memory usage of the program, 
+but there are cases where they are also more time efficient, as demostrated below with a comparison with the 
+equivalent methods of `StatsBase.sample`:
+
+```julia
+julia> using StreamSampling
+
+julia> using BenchmarkTools, Random, StatsBase
+
+julia> rng = Xoshiro(42);
+
+julia> iter = Iterators.filter(x -> x != 10, 1:10^7);
+
+julia> wv(el) = 1.0
+
+julia> @btime itsample($rng, $iter, 10^4, algRSWRSKIP);
+  11.744 ms (5 allocations: 156.39 KiB)
+
+julia> @btime sample($rng, collect($iter), 10^4; replace=true);
+  131.933 ms (20 allocations: 146.91 MiB)
+
+julia> @btime itsample($rng, $iter, 10^4, algL);
+  10.260 ms (3 allocations: 78.22 KiB)
+
+julia> @btime sample($rng, collect($iter), 10^4; replace=false);
+  132.069 ms (27 allocations: 147.05 MiB)
+
+julia> @btime itsample($rng, $iter, $wv, 10^4, algWRSWRSKIP);
+  32.278 ms (18 allocations: 547.34 KiB)
+
+julia> @btime sample($rng, collect($iter), Weights($wv.($iter)), 10^4; replace=true);
+  348.220 ms (49 allocations: 675.21 MiB)
+
+julia> @btime itsample($rng, $iter, $wv, 10^4, algAExpJ);
+  39.965 ms (11 allocations: 234.78 KiB)
+
+julia> @btime sample($rng, collect($iter), Weights($wv.($iter)), 10^4; replace=false);
+  306.039 ms (43 allocations: 370.19 MiB)
+```
+
+