# Module: Daru::Maths::Statistics::Vector

Extended by:
Gem::Deprecate
Included in:
Vector
Defined in:
lib/daru/maths/statistics/vector.rb

## Overview

rubocop:disable Metrics/ModuleLength

## Instance Method Summary collapse

• Calculates the autocorrelation coefficients of the series.

• Provides autocovariance.

• #average_deviation_population(m = nil) ⇒ Object (also: #adp)
• :nocov:.

• Center data by subtracting the mean from each non-nil value.

• #coefficient_of_variation ⇒ Object (also: #cov)
• Retrieves number of cases which comply condition.

• Population covariance with denominator (N).

• #covariance_sample(other) ⇒ Object (also: #covariance)

Sample covariance with denominator (N-1).

• Calculate cumulative sum of Vector.

• Create a summary of count, mean, standard deviation, min and max of the vector in one shot.

• Dichotomize the vector with 0 and 1, based on lowest value.

• Performs the difference of the series.

• Exponential Moving Average.

• Exponential Moving Standard Deviation.

• Exponential Moving Variance.

• Retrieve unique values of non-nil data.

• #frequencies ⇒ Object (also: #freqs)
• Moving Average Convergence-Divergence.

• Maximum element of the vector.

• Return a Vector with the max element and its index.

• #median_absolute_deviation ⇒ Object (also: #mad)
• The percent_change method computes the percent change over the given number of periods.

• #percentile(q, strategy = :midpoint) ⇒ Object (also: #percentil)

Returns the value of the percentile q.

• Calculate the rolling function for a loopback value.

• Calculate rolling non-missing count.

• Calculate rolling max value.

• Calculate rolling average.

• Calculate rolling median.

• Calculate rolling min value.

• Calculate rolling standard deviation.

• Calculate rolling sum.

• Calculate rolling variance.

• Returns an random sample of size n, with replacement, only with non-nil data.

• Returns an random sample of size n, without replacement, only with valid data.

• Calculate skewness using (sigma(xi - mean)^3)/((N)*std_dev_sample^3).

• #standard_deviation_sample(m = nil) ⇒ Object (also: #sds, #sd)
• #standard_error ⇒ Object (also: #se)
• Standardize data.

• #sum_of_squares(m = nil) ⇒ Object (also: #ss)
• Count number of occurrences of each value in the Vector.

• Population variance with denominator (N).

• #variance_sample(m = nil) ⇒ Object (also: #variance)

Sample variance with denominator (N-1).

• Replace each non-nil value in the vector with its percentile.

## Instance Method Details

### #acf(max_lags = nil) ⇒ Object

Calculates the autocorrelation coefficients of the series.

The first element is always 1, since that is the correlation of the series with itself.

Examples:

``````ts = Daru::Vector.new((1..100).map { rand })

ts.acf   # => array with first 21 autocorrelations
ts.acf 3 # => array with first 3 autocorrelations``````
 ``` 616 617 618 619 620 621 622 623 624 625 626 627 628 629``` ```# File 'lib/daru/maths/statistics/vector.rb', line 616 def acf(max_lags=nil) max_lags ||= (10 * Math.log10(size)).to_i (0..max_lags).map do |i| if i.zero? 1.0 else m = mean # can't use Pearson coefficient since the mean for the lagged series should # be the same as the regular series ((self - m) * (lag(i) - m)).sum / variance_sample / (size - 1) end end end```

### #acvf(demean = true, unbiased = true) ⇒ Object

Provides autocovariance.

## Options

• :demean = true; optional. Supply false if series is not to be demeaned

• :unbiased = true; optional. true/false for unbiased/biased form of autocovariance

## Returns

Autocovariance value

 ``` 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662``` ```# File 'lib/daru/maths/statistics/vector.rb', line 641 def acvf(demean=true, unbiased=true) # rubocop:disable Metrics/AbcSize,Metrics/MethodLength opts = { demean: true, unbaised: true }.merge(opts) demean = opts[:demean] unbiased = opts[:unbiased] demeaned_series = demean ? self - mean : self n = (10 * Math.log10(size)).to_i + 1 m = mean d = if unbiased Array.new(size, size) else (1..size).to_a.reverse[0..n] end 0.upto(n - 1).map do |i| (demeaned_series * (lag(i) - m)).sum / d[i] end end```

### #average_deviation_population(m = nil) ⇒ ObjectAlso known as: adp

 ``` 230 231 232 233 234 235 236``` ```# File 'lib/daru/maths/statistics/vector.rb', line 230 def average_deviation_population m=nil must_be_numeric! m ||= mean reject_values(*Daru::MISSING_VALUES).data.inject(0) { |memo, val| (val - m).abs + memo }.quo(size - count_values(*Daru::MISSING_VALUES)) end```

### #box_cox_transformation(lambda) ⇒ Object

:nocov:

 ``` 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310``` ```# File 'lib/daru/maths/statistics/vector.rb', line 296 def box_cox_transformation lambda # :nodoc: must_be_numeric! recode do |x| if !x.nil? if lambda.zero? Math.log(x) else (x ** lambda - 1).quo(lambda) end else nil end end end```

### #center ⇒ Object

Center data by subtracting the mean from each non-nil value.

 ``` 277 278 279``` ```# File 'lib/daru/maths/statistics/vector.rb', line 277 def center self - mean end```

### #coefficient_of_variation ⇒ ObjectAlso known as: cov

 ``` 121 122 123``` ```# File 'lib/daru/maths/statistics/vector.rb', line 121 def coefficient_of_variation standard_deviation_sample / mean end```

### #count(value = false, &block) ⇒ Object

Retrieves number of cases which comply condition. If block given, retrieves number of instances where block returns true. If other values given, retrieves the frequency for this value. If no value given, counts the number of non-nil elements in the Vector.

 ``` 129 130 131 132 133 134 135 136 137``` ```# File 'lib/daru/maths/statistics/vector.rb', line 129 def count value=false, &block if block_given? @data.select(&block).count elsif value count { |val| val == value } else size - indexes(*Daru::MISSING_VALUES).size end end```

### #covariance_population(other) ⇒ Object

Population covariance with denominator (N)

 ``` 179 180 181 182``` ```# File 'lib/daru/maths/statistics/vector.rb', line 179 def covariance_population other size == other.size or raise ArgumentError, 'size of both the vectors must be equal' covariance_sum(other) / (size - count_values(*Daru::MISSING_VALUES)) end```

### #covariance_sample(other) ⇒ ObjectAlso known as: covariance

Sample covariance with denominator (N-1)

 ``` 173 174 175 176``` ```# File 'lib/daru/maths/statistics/vector.rb', line 173 def covariance_sample other size == other.size or raise ArgumentError, 'size of both the vectors must be equal' covariance_sum(other) / (size - count_values(*Daru::MISSING_VALUES) - 1) end```

### #cumsum ⇒ Object

Calculate cumulative sum of Vector

 ``` 665 666 667 668 669 670 671 672 673 674 675 676 677 678``` ```# File 'lib/daru/maths/statistics/vector.rb', line 665 def cumsum result = [] acc = 0 @data.each do |d| if include_with_nan? Daru::MISSING_VALUES, d result << nil else acc += d result << acc end end Daru::Vector.new(result, index: @index) end```

### #describe(methods = nil) ⇒ Object

Create a summary of count, mean, standard deviation, min and max of the vector in one shot.

## Arguments

methods - An array with aggregation methods specified as symbols to be applied to vectors. Default is [:count, :mean, :std, :max, :min]. Methods will be applied in the specified order.

 ``` 47 48 49 50 51``` ```# File 'lib/daru/maths/statistics/vector.rb', line 47 def describe methods=nil methods ||= [:count, :mean, :std, :min, :max] description = methods.map { |m| send(m) } Daru::Vector.new(description, index: methods, name: :statistics) end```

### #dichotomize(low = nil) ⇒ Object

Dichotomize the vector with 0 and 1, based on lowest value. If parameter is defined, this value and lower will be 0 and higher, 1.

 ``` 262 263 264 265 266 267 268 269 270 271 272 273 274``` ```# File 'lib/daru/maths/statistics/vector.rb', line 262 def dichotomize(low=nil) low ||= factors.min recode do |x| if x.nil? nil elsif x > low 1 else 0 end end end```

### #diff(max_lags = 1) ⇒ Daru::Vector

Performs the difference of the series. Note: The first difference of series is X(t) - X(t-1) But, second difference of series is NOT X(t) - X(t-2) It is the first difference of the first difference

# > (X(t) - X(t-1)) - (X(t-1) - X(t-2))

## Arguments

• max_lags: integer, (default: 1), number of differences reqd.

Examples:

Using #diff

``````
ts = Daru::Vector.new((1..10).map { rand })
# => [0.69, 0.23, 0.44, 0.71, ...]

ts.diff   # => [nil, -0.46, 0.21, 0.27, ...]``````

Returns:

 ``` 418 419 420 421 422 423 424 425 426``` ```# File 'lib/daru/maths/statistics/vector.rb', line 418 def diff(max_lags=1) ts = self difference = [] max_lags.times do difference = ts - ts.lag ts = difference end difference end```

### #ema(n = 10, wilder = false) ⇒ Daru::Vector

Exponential Moving Average. Calculates an exponential moving average of the series using a specified parameter. If wilder is false (the default) then the EMA uses a smoothing value of 2 / (n + 1), if it is true then it uses the Welles Wilder smoother of 1 / n.

Warning for EMA usage: EMAs are unstable for small series, as they use a lot more than n observations to calculate. The series is stable if the size of the series is >= 3.45 * (n + 1)

Examples:

Using ema

``````
ts = Daru::Vector.new((1..100).map { rand })
# => [0.577..., 0.123..., 0.173..., 0.233..., ...]

# first 9 observations are nil
ts.ema   # => [ ... nil, 0.455... , 0.395..., 0.323..., ... ]``````

Parameters:

• n (Integer) (defaults to: 10)

(10) Loopback length.

• wilder (TrueClass, FalseClass) (defaults to: false)

(false) If true, 1/n value is used for smoothing; if false, uses 2/(n+1) value

Returns:

• Contains EMA

 ``` 502 503 504 505 506 507 508 509 510 511 512 513 514 515``` ```# File 'lib/daru/maths/statistics/vector.rb', line 502 def ema(n=10, wilder=false) # rubocop:disable Metrics/AbcSize smoother = wilder ? 1.0 / n : 2.0 / (n + 1) # need to start everything from the first non-nil observation start = @data.index { |i| !i.nil? } # first n - 1 observations are nil base = [nil] * (start + n - 1) # nth observation is just a moving average base << @data[start...(start + n)].inject(0.0) { |s, a| a.nil? ? s : s + a } / n (start + n).upto size - 1 do |i| base << self[i] * smoother + (1 - smoother) * base.last end Daru::Vector.new(base, index: @index, name: @name) end```

### #emsd(n = 10, wilder = false) ⇒ Daru::Vector

Exponential Moving Standard Deviation. Calculates an exponential moving standard deviation of the series using a specified parameter. If wilder is false (the default) then the EMSD uses a smoothing value of 2 / (n + 1), if it is true then it uses the Welles Wilder smoother of 1 / n.

Examples:

Using emsd

``````
ts = Daru::Vector.new((1..100).map { rand })
# => [0.400..., 0.727..., 0.862..., 0.013..., ...]

# first 9 observations are nil
ts.emsd   # => [ ... nil, 0.285... , 0.258..., 0.243..., ...]``````

Parameters:

• n (Integer) (defaults to: 10)

(10) Loopback length.

• wilder (TrueClass, FalseClass) (defaults to: false)

(false) If true, 1/n value is used for smoothing; if false, uses 2/(n+1) value

Returns:

• contains EMSD

 ``` 573 574 575 576 577 578 579 580``` ```# File 'lib/daru/maths/statistics/vector.rb', line 573 def emsd(n=10, wilder=false) result = [] emv_return = emv(n, wilder) emv_return.each do |d| result << (d.nil? ? nil : Math.sqrt(d)) end Daru::Vector.new(result, index: @index, name: @name) end```

### #emv(n = 10, wilder = false) ⇒ Daru::Vector

Exponential Moving Variance. Calculates an exponential moving variance of the series using a specified parameter. If wilder is false (the default) then the EMV uses a smoothing value of 2 / (n + 1), if it is true then it uses the Welles Wilder smoother of 1 / n.

Examples:

Using emv

``````
ts = Daru::Vector.new((1..100).map { rand })
# => [0.047..., 0.23..., 0.836..., 0.845..., ...]

# first 9 observations are nil
ts.emv   # => [ ... nil, 0.073... , 0.082..., 0.080..., ...]``````

Parameters:

• n (Integer) (defaults to: 10)

(10) Loopback length.

• wilder (TrueClass, FalseClass) (defaults to: false)

(false) If true, 1/n value is used for smoothing; if false, uses 2/(n+1) value

Returns:

• contains EMV

 ``` 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552``` ```# File 'lib/daru/maths/statistics/vector.rb', line 536 def emv(n=10, wilder=false) # rubocop:disable Metrics/AbcSize smoother = wilder ? 1.0 / n : 2.0 / (n + 1) # need to start everything from the first non-nil observation start = @data.index { |i| !i.nil? } # first n - 1 observations are nil var_base = [nil] * (start + n - 1) mean_base = [nil] * (start + n - 1) mean_base << @data[start...(start + n)].inject(0.0) { |s, a| a.nil? ? s : s + a } / n # nth observation is just a moving variance_population var_base << @data[start...(start + n)].inject(0.0) { |s,x| x.nil? ? s : s + (x - mean_base.last)**2 } / n (start + n).upto size - 1 do |i| last = mean_base.last mean_base << self[i] * smoother + (1 - smoother) * last var_base << (1 - smoother) * var_base.last + smoother * (self[i] - last) * (self[i] - mean_base.last) end Daru::Vector.new(var_base, index: @index, name: @name) end```

### #factors ⇒ Object

Retrieve unique values of non-nil data

 ``` 69 70 71``` ```# File 'lib/daru/maths/statistics/vector.rb', line 69 def factors reject_values(*Daru::MISSING_VALUES).uniq.reset_index! end```

### #frequencies ⇒ ObjectAlso known as: freqs

 ``` 93 94 95 96 97 98 99``` ```# File 'lib/daru/maths/statistics/vector.rb', line 93 def frequencies Daru::Vector.new( @data.each_with_object(Hash.new(0)) do |element, hash| hash[element] += 1 unless element.nil? end ) end```

### #kurtosis(m = nil) ⇒ Object

 ``` 220 221 222 223 224 225 226 227 228``` ```# File 'lib/daru/maths/statistics/vector.rb', line 220 def kurtosis m=nil if @data.respond_to? :kurtosis @data.kurtosis else m ||= mean fo = @data.inject(0) { |a, x| a + ((x - m) ** 4) } fo.quo((size - indexes(*Daru::MISSING_VALUES).size) * standard_deviation_sample(m) ** 4) - 3 end end```

### #macd(fast = 12, slow = 26, signal = 9) ⇒ Object

Moving Average Convergence-Divergence. Calculates the MACD (moving average convergence-divergence) of the time series - this is a comparison of a fast EMA with a slow EMA.

## Arguments

• fast: integer, (default = 12) - fast component of MACD

• slow: integer, (default = 26) - slow component of MACD

• signal: integer, (default = 9) - signal component of MACD

## Usage

``````ts = Daru::Vector.new((1..100).map { rand })
# => [0.69, 0.23, 0.44, 0.71, ...]
ts.macd(13)``````

## Returns

Array of two Daru::Vectors - comparison of fast EMA with slow and EMA with signal value

 ``` 601 602 603 604``` ```# File 'lib/daru/maths/statistics/vector.rb', line 601 def macd(fast=12, slow=26, signal=9) series = ema(fast) - ema(slow) [series, series.ema(signal)] end```

### #max(return_type = :stored_type) ⇒ Object

Maximum element of the vector.

Parameters:

• return_type (Symbol) (defaults to: :stored_type)

Data type of the returned value. Defaults to returning only the maximum number but passing :vector will return a Daru::Vector with the index of the corresponding maximum value.

 ``` 78 79 80 81 82 83 84 85``` ```# File 'lib/daru/maths/statistics/vector.rb', line 78 def max return_type=:stored_type max_value = @data.max if return_type == :vector Daru::Vector.new({index_of(max_value) => max_value}, name: @name, dtype: @dtype) else max_value end end```

### #max_index ⇒ Daru::Vector

Return a Vector with the max element and its index.

Returns:

 ``` 89 90 91``` ```# File 'lib/daru/maths/statistics/vector.rb', line 89 def max_index max :vector end```

### #mean ⇒ Object

 ``` 10 11 12``` ```# File 'lib/daru/maths/statistics/vector.rb', line 10 def mean @data.mean end```

### #median ⇒ Object

 ``` 30 31 32``` ```# File 'lib/daru/maths/statistics/vector.rb', line 30 def median @data.respond_to?(:median) ? @data.median : percentile(50) end```

### #median_absolute_deviation ⇒ ObjectAlso known as: mad

 ``` 53 54 55 56``` ```# File 'lib/daru/maths/statistics/vector.rb', line 53 def median_absolute_deviation m = median recode { |val| (val - m).abs }.median end```

### #min ⇒ Object

 ``` 22 23 24``` ```# File 'lib/daru/maths/statistics/vector.rb', line 22 def min @data.min end```

### #mode ⇒ Object

 ``` 34 35 36 37``` ```# File 'lib/daru/maths/statistics/vector.rb', line 34 def mode mode = frequencies.to_h.select { |_,v| v == frequencies.max }.keys mode.size > 1 ? Daru::Vector.new(mode) : mode.first end```

### #percent_change(periods = 1) ⇒ Object

The percent_change method computes the percent change over the given number of periods.

Examples:

``````
vector = Daru::Vector.new([4,6,6,8,10],index: ['a','f','t','i','k'])
vector.percent_change
#=>
#   <Daru::Vector:28713060 @name = nil size: 5 >
#              nil
#   a
#   f	   0.5
#   t	   0.0
#   i	   0.3333333333333333
#   k          0.25``````

Parameters:

• periods (Integer) (defaults to: 1)

(1) number of nils to insert at the beginning.

 ``` 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398``` ```# File 'lib/daru/maths/statistics/vector.rb', line 383 def percent_change periods=1 must_be_numeric! prev = nil arr = @data.each_with_index.map do |cur, i| if i < periods || include_with_nan?(Daru::MISSING_VALUES, cur) || include_with_nan?(Daru::MISSING_VALUES, prev) nil else (cur - prev) / prev.to_f end.tap { prev = cur if cur } end Daru::Vector.new(arr, index: @index, name: @name) end```

### #percentile(q, strategy = :midpoint) ⇒ ObjectAlso known as: percentil

Returns the value of the percentile q

Accepts an optional second argument specifying the strategy to interpolate when the requested percentile lies between two data points a and b Valid strategies are:

• :midpoint (Default): (a + b) / 2

• :linear : a + (b - a) * d where d is the decimal part of the index between a and b.

## References

This is the NIST recommended method (en.wikipedia.org/wiki/Percentile#NIST_method)

 ``` 248 249 250 251 252 253 254 255 256 257``` ```# File 'lib/daru/maths/statistics/vector.rb', line 248 def percentile(q, strategy=:midpoint) case strategy when :midpoint midpoint_percentile(q) when :linear linear_percentile(q) else raise ArgumentError, "Unknown strategy #{strategy}" end end```

### #product ⇒ Object

 ``` 18 19 20``` ```# File 'lib/daru/maths/statistics/vector.rb', line 18 def product @data.product end```

### #proportion(value = 1) ⇒ Object

 ``` 148 149 150``` ```# File 'lib/daru/maths/statistics/vector.rb', line 148 def proportion value=1 frequencies[value].quo(size - count_values(*Daru::MISSING_VALUES)).to_f end```

### #proportions ⇒ Object

 ``` 104 105 106 107 108 109``` ```# File 'lib/daru/maths/statistics/vector.rb', line 104 def proportions len = size - count_values(*Daru::MISSING_VALUES) frequencies.to_h.each_with_object({}) do |(el, count), hash| hash[el] = count / len end end```

### #range ⇒ Object

 ``` 26 27 28``` ```# File 'lib/daru/maths/statistics/vector.rb', line 26 def range max - min end```

### #ranked ⇒ Object

 ``` 111 112 113 114 115 116 117 118 119``` ```# File 'lib/daru/maths/statistics/vector.rb', line 111 def ranked sum = 0 r = frequencies.to_h.sort.each_with_object({}) do |(el, count), memo| memo[el] = ((sum + 1) + (sum + count)).quo(2) sum += count end recode { |e| r[e] } end```

### #rolling(function, n = 10) ⇒ Daru::Vector

Calculate the rolling function for a loopback value.

Examples:

Using #rolling

``````ts = Daru::Vector.new((1..100).map { rand })
# => [0.69, 0.23, 0.44, 0.71, ...]
# first 9 observations are nil
ts.rolling(:mean)    # => [ ... nil, 0.484... , 0.445... , 0.513 ... , ... ]``````

Parameters:

• function (Symbol)

The rolling function to be applied. Can be any function applicatble to Daru::Vector (:mean, :median, :count, :min, :max, etc.)

• n (Integer) (defaults to: 10)

(10) A non-negative value which serves as the loopback length.

Returns:

• Vector containin rolling calculations.

 ``` 440 441 442 443 444 445 446 447``` ```# File 'lib/daru/maths/statistics/vector.rb', line 440 def rolling function, n=10 Daru::Vector.new( [nil] * (n - 1) + (0..(size - n)).map do |i| Daru::Vector.new(@data[i...(i + n)]).send(function) end, index: @index ) end```

### #rolling_count ⇒ Object

Calculate rolling non-missing count

Parameters:

• n (Integer)

(10) Loopback length

 ``` 473 474 475 476 477``` ```# File 'lib/daru/maths/statistics/vector.rb', line 473 [:count, :mean, :median, :max, :min, :sum, :std, :variance].each do |meth| define_method("rolling_#{meth}".to_sym) do |n=10| rolling(meth, n) end end```

### #rolling_max ⇒ Object

Calculate rolling max value

Parameters:

• n (Integer)

(10) Loopback length

 ``` 473 474 475 476 477``` ```# File 'lib/daru/maths/statistics/vector.rb', line 473 [:count, :mean, :median, :max, :min, :sum, :std, :variance].each do |meth| define_method("rolling_#{meth}".to_sym) do |n=10| rolling(meth, n) end end```

### #rolling_mean ⇒ Object

Calculate rolling average

Parameters:

• n (Integer)

(10) Loopback length

 ``` 473 474 475 476 477``` ```# File 'lib/daru/maths/statistics/vector.rb', line 473 [:count, :mean, :median, :max, :min, :sum, :std, :variance].each do |meth| define_method("rolling_#{meth}".to_sym) do |n=10| rolling(meth, n) end end```

### #rolling_median ⇒ Object

Calculate rolling median

Parameters:

• n (Integer)

(10) Loopback length

 ``` 473 474 475 476 477``` ```# File 'lib/daru/maths/statistics/vector.rb', line 473 [:count, :mean, :median, :max, :min, :sum, :std, :variance].each do |meth| define_method("rolling_#{meth}".to_sym) do |n=10| rolling(meth, n) end end```

### #rolling_min ⇒ Object

Calculate rolling min value

Parameters:

• n (Integer)

(10) Loopback length

 ``` 473 474 475 476 477``` ```# File 'lib/daru/maths/statistics/vector.rb', line 473 [:count, :mean, :median, :max, :min, :sum, :std, :variance].each do |meth| define_method("rolling_#{meth}".to_sym) do |n=10| rolling(meth, n) end end```

### #rolling_std ⇒ Object

Calculate rolling standard deviation

Parameters:

• n (Integer)

(10) Loopback length

 ``` 473 474 475 476 477``` ```# File 'lib/daru/maths/statistics/vector.rb', line 473 [:count, :mean, :median, :max, :min, :sum, :std, :variance].each do |meth| define_method("rolling_#{meth}".to_sym) do |n=10| rolling(meth, n) end end```

### #rolling_sum ⇒ Object

Calculate rolling sum

Parameters:

• n (Integer)

(10) Loopback length

 ``` 473 474 475 476 477``` ```# File 'lib/daru/maths/statistics/vector.rb', line 473 [:count, :mean, :median, :max, :min, :sum, :std, :variance].each do |meth| define_method("rolling_#{meth}".to_sym) do |n=10| rolling(meth, n) end end```

### #rolling_variance ⇒ Object

Calculate rolling variance

Parameters:

• n (Integer)

(10) Loopback length

 ``` 473 474 475 476 477``` ```# File 'lib/daru/maths/statistics/vector.rb', line 473 [:count, :mean, :median, :max, :min, :sum, :std, :variance].each do |meth| define_method("rolling_#{meth}".to_sym) do |n=10| rolling(meth, n) end end```

### #sample_with_replacement(sample = 1) ⇒ Object

Returns an random sample of size n, with replacement, only with non-nil data.

In all the trails, every item have the same probability of been selected.

 ``` 342 343 344 345 346 347 348 349 350``` ```# File 'lib/daru/maths/statistics/vector.rb', line 342 def sample_with_replacement(sample=1) if @data.respond_to? :sample_with_replacement @data.sample_with_replacement sample else valid = indexes(*Daru::MISSING_VALUES).empty? ? self : reject_values(*Daru::MISSING_VALUES) vds = valid.size (0...sample).collect { valid[rand(vds)] } end end```

### #sample_without_replacement(sample = 1) ⇒ Object

Returns an random sample of size n, without replacement, only with valid data.

Every element could only be selected once.

A sample of the same size of the vector is the vector itself.

 ``` 358 359 360 361 362 363 364``` ```# File 'lib/daru/maths/statistics/vector.rb', line 358 def sample_without_replacement(sample=1) if @data.respond_to? :sample_without_replacement @data.sample_without_replacement sample else raw_sample_without_replacement(sample) end end```

### #skew(m = nil) ⇒ Object

Calculate skewness using (sigma(xi - mean)^3)/((N)*std_dev_sample^3)

 ``` 210 211 212 213 214 215 216 217 218``` ```# File 'lib/daru/maths/statistics/vector.rb', line 210 def skew m=nil if @data.respond_to? :skew @data.skew else m ||= mean th = @data.inject(0) { |memo, val| memo + ((val - m)**3) } th.quo((size - indexes(*Daru::MISSING_VALUES).size) * (standard_deviation_sample(m)**3)) end end```

### #standard_deviation_population(m = nil) ⇒ ObjectAlso known as: sdp

 ``` 191 192 193 194 195 196 197 198``` ```# File 'lib/daru/maths/statistics/vector.rb', line 191 def standard_deviation_population m=nil m ||= mean if @data.respond_to? :standard_deviation_population @data.standard_deviation_population(m) else Math.sqrt(variance_population(m)) end end```

### #standard_deviation_sample(m = nil) ⇒ ObjectAlso known as: sds, sd

 ``` 200 201 202 203 204 205 206 207``` ```# File 'lib/daru/maths/statistics/vector.rb', line 200 def standard_deviation_sample m=nil m ||= mean if @data.respond_to? :standard_deviation_sample @data.standard_deviation_sample m else Math.sqrt(variance_sample(m)) end end```

### #standard_error ⇒ ObjectAlso known as: se

 ``` 60 61 62``` ```# File 'lib/daru/maths/statistics/vector.rb', line 60 def standard_error standard_deviation_sample/Math.sqrt(size - count_values(*Daru::MISSING_VALUES)) end```

### #standardize(use_population = false) ⇒ Object

Standardize data.

## Arguments

• use_population - Pass as true if you want to use population

standard deviation instead of sample standard deviation.

 ``` 287 288 289 290 291 292 293``` ```# File 'lib/daru/maths/statistics/vector.rb', line 287 def standardize use_population=false m ||= mean sd = use_population ? sdp : sds return Daru::Vector.new([nil]*size) if m.nil? || sd == 0.0 vector_standardized_compute m, sd end```

### #sum ⇒ Object

 ``` 14 15 16``` ```# File 'lib/daru/maths/statistics/vector.rb', line 14 def sum @data.sum end```

### #sum_of_squared_deviation ⇒ Object

 ``` 64 65 66``` ```# File 'lib/daru/maths/statistics/vector.rb', line 64 def sum_of_squared_deviation (@data.inject(0) { |a,x| x**2 + a } - (sum**2).quo(size - count_values(*Daru::MISSING_VALUES)).to_f).to_f end```

### #sum_of_squares(m = nil) ⇒ ObjectAlso known as: ss

 ``` 184 185 186 187 188 189``` ```# File 'lib/daru/maths/statistics/vector.rb', line 184 def sum_of_squares(m=nil) m ||= mean reject_values(*Daru::MISSING_VALUES).data.inject(0) { |memo, val| memo + (val - m)**2 } end```

### #value_counts ⇒ Object

Count number of occurrences of each value in the Vector

 ``` 140 141 142 143 144 145 146``` ```# File 'lib/daru/maths/statistics/vector.rb', line 140 def value_counts values = @data.each_with_object(Hash.new(0)) do |d, memo| memo[d] += 1 end Daru::Vector.new(values) end```

### #variance_population(m = nil) ⇒ Object

Population variance with denominator (N)

 ``` 163 164 165 166 167 168 169 170``` ```# File 'lib/daru/maths/statistics/vector.rb', line 163 def variance_population m=nil m ||= mean if @data.respond_to? :variance_population @data.variance_population m else sum_of_squares(m).quo(size - count_values(*Daru::MISSING_VALUES)).to_f end end```

### #variance_sample(m = nil) ⇒ ObjectAlso known as: variance

Sample variance with denominator (N-1)

 ``` 153 154 155 156 157 158 159 160``` ```# File 'lib/daru/maths/statistics/vector.rb', line 153 def variance_sample m=nil m ||= mean if @data.respond_to? :variance_sample @data.variance_sample m else sum_of_squares(m).quo(size - count_values(*Daru::MISSING_VALUES) - 1) end end```

### #vector_centered_compute(m) ⇒ Object

 ``` 328 329 330 331 332 333 334 335``` ```# File 'lib/daru/maths/statistics/vector.rb', line 328 def vector_centered_compute(m) if @data.respond_to? :vector_centered_compute @data.vector_centered_compute(m) else Daru::Vector.new @data.collect { |x| x.nil? ? nil : x.to_f-m }, index: index, name: name, dtype: dtype end end```

### #vector_percentile ⇒ Object

Replace each non-nil value in the vector with its percentile.

 ``` 314 315 316 317``` ```# File 'lib/daru/maths/statistics/vector.rb', line 314 def vector_percentile c = size - indexes(*Daru::MISSING_VALUES).size ranked.recode! { |i| i.nil? ? nil : (i.quo(c)*100).to_f } end```

### #vector_standardized_compute(m, sd) ⇒ Object

 ``` 319 320 321 322 323 324 325 326``` ```# File 'lib/daru/maths/statistics/vector.rb', line 319 def vector_standardized_compute(m,sd) if @data.respond_to? :vector_standardized_compute @data.vector_standardized_compute(m,sd) else Daru::Vector.new @data.collect { |x| x.nil? ? nil : (x.to_f - m).quo(sd) }, index: index, name: name, dtype: dtype end end```