Docs: spellcheck

docs/content/DescriptiveStatistics.fsx

@@ -22,7 +22,7 @@ Univariate Statistical Analysis
 
 The primary class for statistical analysis is `Statistics` which provides common
 descriptive statics as static extension methods to `IEnumerable<double>` sequences.
-However, various statstics can be computed much more efficiently if the data source
+However, various statistics can be computed much more efficiently if the data source
 has known properties or structure, that's why the following classes provide specialized
 static implementations:
 
@@ -57,7 +57,7 @@ in one pass, is provided by the `DescriptiveStatistics` class:
 Minimum & Maximum
 -----------------
 
-The minimum and maximum values of a sample set can be evaluted with the `Minimum` and `Maximum`
+The minimum and maximum values of a sample set can be evaluated with the `Minimum` and `Maximum`
 functions of all four classes: `Statistics`, `ArrayStatistics`, `SortedArrayStatistics`
 and `StreamingStatistics`. The one in `SortedArrayStatistics` is the fastest with constant
 time complexity, but expects the array to be sorted ascendingly.
@@ -184,9 +184,9 @@ If the samples are sorted ascendingly, this is trivial and can be evaluated in c
 which is what the `SortedArrayStatistics` implementation does.
 
 If you have the samples in an array which is not (guaranteed to be) sorted,
-but if it is ok if the array does incrementally get sorted over mutliple calls,
-you can also use the following inplace implementation. It is usually faster
-than fully sorting the array, unless you need to compute it for more than a handfull orders.
+but if it is fine if the array does incrementally get sorted over multiple calls,
+you can also use the following in-place implementation. It is usually faster
+than fully sorting the array, unless you need to compute it for more than a handful orders.
 
 `ArrayStatistics.OrderStatisticInplace(data, order)`
 
@@ -218,7 +218,7 @@ os 750
 
 Median is a robust indicator of central tendency and much less affected by outliers
 than the sample mean. The median is estimated by the value exactly in the middle of
-the sorted set of samples and thus seperating the higher half of the data from the lower half.
+the sorted set of samples and thus separating the higher half of the data from the lower half.
 
 `Statistics.Median(data)`  
 `SortedArrayStatistics.Median(data)`  
@@ -259,7 +259,7 @@ Statistics.UpperQuartile whiteNoise
 
 (**
 Using that data we can provide a useful set of indicators usually named 5-number summary,
-which consists of the minimum value, the lower quartile, the median, the uppper quartile and
+which consists of the minimum value, the lower quartile, the median, the upper quartile and
 the maximum value. All these values can be visualized in the popular box plot diagrams.
 
 `Statistics.FiveNumberSummary(data)`  
@@ -289,7 +289,7 @@ Statistics.InterquartileRange whiteNoise
 (**
 #### Percentiles
 
-Precentiles extend the concept further by grouping the sorted values into 100
+Percentiles extend the concept further by grouping the sorted values into 100
 equal groups and looking at the 101 places (0,1,..,100) between and around them.
 The 0-percentile represents the minimum value, 25 the first quartile, 50 the median,
 75 the upper quartile and 100 the maximum value.
@@ -350,7 +350,7 @@ The `QuantileDefinition` enumeration has the following options:
 * **R3**, SAS2, Nearest
 * **R4**, SAS1, California
 * **R5**, Hydrology, Hazen
-* **R6**, SAS4, Nust, Weibull, SPSS
+* **R6**, SAS4, Nist, Weibull, SPSS
 * **R7**, Excel, Mode, S
 * **R8**, Median, Default
 * **R9**, Normal
@@ -378,7 +378,7 @@ Similar to `QuantileDefinition`, the `RankDefinition` enumeration controls how t
 * **First**: Permutation with increasing values at each index of ties.
 * **EmpiricalCDF**
 
-`Statistics.Ranks(data, defintion)`  
+`Statistics.Ranks(data, definition)`  
 `SortedArrayStatistics.Ranks(data, definition)`  
 `ArrayStatistics.RanksInplace(data, definition)`
 *)
@@ -436,7 +436,7 @@ let eicdf = Statistics.empiricalInvCDFFunc whiteNoise
 Histograms
 ----------
 
-A histrogram can be computed using the [Histogram][hist] class. Its constructor takes
+A histogram can be computed using the [Histogram][hist] class. Its constructor takes
 the samples enumerable, the number of buckets to create, plus optionally the range
 (minimum, maximum) of the sample data if available.
 

docs/content/Distance.fsx

@@ -101,7 +101,7 @@ Manhattan Distance
 
 <img src="img/DistanceManhattan.png" style="width:87px; height:87px; float:left; margin:10px 10px 10px 0;" />
 
-The manhattan distance is the $L_1$-norm of the difference, a special case of the Minkowski distance with p=1
+The Manhattan distance is the $L_1$-norm of the difference, a special case of the Minkowski distance with p=1
 and equivalent to the sum of absolute difference.
 
 $$$
@@ -116,7 +116,7 @@ Chebyshev Distance
 
 <img src="img/DistanceChebyshev.png" style="width:87px; height:87px; float:left; margin:10px 10px 10px 0;" />
 
-The chebyshev distance is the $L_\infty$-norm of the difference, a special case of the Minkowski distance
+The Chebyshev distance is the $L_\infty$-norm of the difference, a special case of the Minkowski distance
 where p goes to infinity. It is also known as Chessboard distance. 
 
 $$$
@@ -131,7 +131,7 @@ Minkowski Distance
 
 <img src="img/DistanceMinkowski3.png" style="width:87px; height:87px; float:left; margin:10px 10px 10px 0;" />
 
-The minkovski distance is the generalized $L_p$-norm of the difference.
+The Minkowski distance is the generalized $L_p$-norm of the difference.
 The contour plot on the left demonstrates the case of p=3.
 
 $$$
@@ -146,7 +146,7 @@ Canberra Distance
 
 <img src="img/DistanceCanberra.png" style="width:87px; height:87px; float:left; margin:10px 10px 10px 0;" />
 
-The Canberra distance is a weighted version of the manhattan distance, introduced and refined 1967 by Lance, Williams and Adkins.
+The Canberra distance is a weighted version of the Manhattan distance, introduced and refined 1967 by Lance, Williams and Adkins.
 It is often used for data scattered around an origin, as it is biased for measures around the origin and very sensitive for values close to zero.
 
 $$$

docs/content/Functions.fsx

@@ -276,7 +276,7 @@ x \mapsto \mathrm{K}_1(x)
 
 * `BesselK1e(x)`
 
-Exponentionally scaled modified Bessel function of the second kind, order 1.
+Exponentially scaled modified Bessel function of the second kind, order 1.
 
 $$$
 x \mapsto e^x\mathrm{K}_1(x)
@@ -284,7 +284,7 @@ x \mapsto e^x\mathrm{K}_1(x)
 
 #### Modified Struve functions
 
-Struve functions are solutions $y(x)$ of the non-homogenous Bessel's differential equation
+Struve functions are solutions $y(x)$ of the non-homogeneous Bessel's differential equation
 
 $$$
 x^2\frac{\mathrm{d}^2y}{\mathrm{d}x^2}+x\frac{\mathrm{d}y}{\mathrm{d}x}+(x^2-\alpha^2)y = \frac{4(\frac{x}{2})^{\alpha+1}}{\sqrt{\pi}\Gamma(\alpha+\frac{1}{2})}

docs/content/IntegralTransforms.fsx

@@ -19,14 +19,14 @@ is to be used can be specified by an additional _options_ parameter.
 Fourier Space: Discrete Fourier Transform and FFT
 -------------------------------------------------
 
-Wikipedia has an extensive [article on the discrete fourier transform (DFT)](http://en.wikipedia.org/wiki/Discrete_Fourier_transform).
+Wikipedia has an extensive [article on the discrete Fourier transform (DFT)](http://en.wikipedia.org/wiki/Discrete_Fourier_transform).
 We provide implementations of the following algorithms:
 
 * *Naive Discrete Fourier Transform (DFT):* Out-place transform for arbitrary vector lengths. Mainly intended for verifying faster algorithms: _[NaiveForward](http://api.mathdotnet.com/Numerics/MathNet.Numerics.IntegralTransforms.Algorithms/DiscreteFourierTransform.htm#NaiveForward)_, _[NaiveInverse](http://api.mathdotnet.com/Numerics/MathNet.Numerics.IntegralTransforms.Algorithms/DiscreteFourierTransform.htm#NaiveInverse)_
 
-* *Radix-2 Fast Fourier Transform (FFT):* In-place fast fourier transform for vectors with a power-of-two length (Radix-2): _[Radix2Forward](http://api.mathdotnet.com/Numerics/MathNet.Numerics.IntegralTransforms.Algorithms/DiscreteFourierTransform.htm#Radix2Forward)_, _[url:Radix2Inverse](http://api.mathdotnet.com/Numerics/MathNet.Numerics.IntegralTransforms.Algorithms/DiscreteFourierTransform.htm#Radix2Inverse)_
+* *Radix-2 Fast Fourier Transform (FFT):* In-place fast Fourier transform for vectors with a power-of-two length (Radix-2): _[Radix2Forward](http://api.mathdotnet.com/Numerics/MathNet.Numerics.IntegralTransforms.Algorithms/DiscreteFourierTransform.htm#Radix2Forward)_, _[url:Radix2Inverse](http://api.mathdotnet.com/Numerics/MathNet.Numerics.IntegralTransforms.Algorithms/DiscreteFourierTransform.htm#Radix2Inverse)_
 
-* *Bluestein Fast Fourier Transform (FFT):* In-place fast fourier transform for arbitrary vector lengths: _[BluesteinForward](http://api.mathdotnet.com/Numerics/MathNet.Numerics.IntegralTransforms.Algorithms/DiscreteFourierTransform.htm#BluesteinForward)_, _[url:BluesteinInverse](http://api.mathdotnet.com/Numerics/MathNet.Numerics.IntegralTransforms.Algorithms/DiscreteFourierTransform.htm#BluesteinInverse)_
+* *Bluestein Fast Fourier Transform (FFT):* In-place fast Fourier transform for arbitrary vector lengths: _[BluesteinForward](http://api.mathdotnet.com/Numerics/MathNet.Numerics.IntegralTransforms.Algorithms/DiscreteFourierTransform.htm#BluesteinForward)_, _[url:BluesteinInverse](http://api.mathdotnet.com/Numerics/MathNet.Numerics.IntegralTransforms.Algorithms/DiscreteFourierTransform.htm#BluesteinInverse)_
 
 Furthermore, the _[Transform](http://api.mathdotnet.com/Numerics/MathNet.Numerics.IntegralTransforms/Transform.htm)_ class provides a shortcut for the Bluestein FFT using static methods which are even easier to use: _[FourierForward](http://api.mathdotnet.com/Numerics/MathNet.Numerics.IntegralTransforms/Transform.htm#FourierForward)_, _[FourierInverse](http://api.mathdotnet.com/Numerics/MathNet.Numerics.IntegralTransforms/Transform.htm#FourierInverse)_.
 
@@ -47,12 +47,12 @@ Fourier Options:
 * *AsymmetricScaling:* Set this flag to suppress scaling on the forward transformation but scale the inverse transform with 1/N. 
 * *NoScaling:* Set this flag to suppress scaling for both forward and inverse transformation. Note that in this case if you apply first the forward and then inverse transformation you won't get back the original signal (by factor N/2).
 * *InverseExponent:* Uses the positive instead of the negative sign in the forward exponent, and the negative (instead of positive) exponent in the inverse transformation.
-* *Matlab:* Use this flag if you need Matlab compatibility. Equals to setting the _AsymmetricScaling_ flag. This matches the definition used in the [url:wikipedia article|http://en.wikipedia.org/wiki/Discrete_Fourier_transform].
+* *Matlab:* Use this flag if you need MATLAB compatibility. Equals to setting the _AsymmetricScaling_ flag. This matches the definition used in the [url:wikipedia article|http://en.wikipedia.org/wiki/Discrete_Fourier_transform].
 * *NumericalRecipes:* Use this flag if you need Numerical Recipes compatibility. Equal to setting both the _InverseExponent_ and the _NoScaling_ flags.
 
-Useful symmetries of the fourier transform:
+Useful symmetries of the Fourier transform:
 
-* h(t) is real valued <=> real part of H(f) is even, imgainary part of H(f) is odd
+* h(t) is real valued <=> real part of H(f) is even, imaginary part of H(f) is odd
 * h(t) is imaginary valued <=> real part of H(f) is odd, imaginary part of H(f) is even
 * h(t) is even <=> H(f) is even
 * h(t) is odd <=> H(f) is odd

docs/content/RandomAndDistributions.fsx

@@ -87,7 +87,7 @@ inherit from `System.Random`, are fully compatible to it and can also be used ex
     var sample = random.NextDouble();
 
 However, unlike System.Random they can be made thread safe, use much more reasonable
-default seeds and have some convinient extra routines. The `SystemRandomSource` class that
+default seeds and have some convenient extra routines. The `SystemRandomSource` class that
 was used above uses System.Random to generate random numbers internally - but with all the extras.
 
 
@@ -118,7 +118,7 @@ so our crypto random source does not accept a seed.
 
 In the code samples above we did not provide a seed, so a default seed was used.
 If no seed is provided, `System.Random` uses a time based seed equivalent to the
-one below. This means that all instances created within a short timeframe
+one below. This means that all instances created within a short time-frame
 (which typically spans about a thousand CPU clock cycles) will generate
 exactly the same sequence. This can happen easily e.g. in parallel computing
 and is often unwanted. That's why all Math.NET Numerics RNGs are by default
@@ -155,10 +155,10 @@ Up to now we've used only `SystemRandomSource`, but there's much more:
 * `CryptoRandomSource`: Wraps the .NET BCL RNGCryptoServiceProvider. *Not available in portable builds.*
 * `MersenneTwister`: Mersenne Twister 19937 generator
 * `Xorshift`: Multiply-with-carry XOR-shift generator
-* `Mcg31m1`: Multiplicative congruental generator using a modulus of 2^31-1 and a multiplier of 1132489760
-* `Mcg59`: Multiplicative congruental generator using a modulus of 2^59 and a multiplier of 13^13
-* `WH1982`: Wichmann-Hill's 1982 combined multiplicative congruental generator
-* `WH2006`: Wichmann-Hill's 2006 combined multiplicative congruental generator
+* `Mcg31m1`: Multiplicative congruential generator using a modulus of 2^31-1 and a multiplier of 1132489760
+* `Mcg59`: Multiplicative congruential generator using a modulus of 2^59 and a multiplier of 13^13
+* `WH1982`: Wichmann-Hill's 1982 combined multiplicative congruential generator
+* `WH2006`: Wichmann-Hill's 2006 combined multiplicative congruential generator
 * `Mrg32k3a`: 32-bit combined multiple recursive generator with 2 components of order 3
 * `Palf`: Parallel Additive Lagged Fibonacci generator
 
@@ -261,7 +261,7 @@ let cauchy = Cauchy(0.0, 1.0, Random.mrg32k3aWith 10 false)
 let poisson = Poisson(3.0)
 let geometric = Geometric(0.8, Random.system())
 
-// sample some random rumbers from these distributions
+// sample some random numbers from these distributions
 let continuous =
   [ yield normal.Sample()
     yield exponential.Sample()

docs/content/index.fsx

@@ -30,7 +30,7 @@ Supported Platforms:
 
 - .Net 4.0, .Net 3.5 and Mono: Windows, Linux and Mac.
 - PCL Portable Profiles 47 and 136: Silverlight 5, Windows Phone 8, .NET for Windows Store apps (Metro).
-- PCL/Xamarin: Andoid, iOS
+- PCL/Xamarin: Android, iOS
 
 Building Math.NET Numerics
 --------------------------