• Statistical conventions:
  Weighting factor options, Effective sample number, Denominator options
• Means:
  Arithmetic mean,   geometric mean,   harmonic mean,   generalised mean (power mean),   interquartile mean,   root mean square,   median,   subtract the arithmetic mean from a data array
• Standard Deviation, Standard Error, Variance, Skewness and Kurtosis:
  Standard deviation,   Standard error,   Volatility,   Variance,   Coefficient of variation,   Skewness,   Kurtosis
• Data standardisation:
  Standardisation to a mean of zero and standard deviation of unity,    Scaling to new mean and standard deviation,    Wilson-Hilferty Transform
• Correlation and Covariance:
  Linear correlation coefficient,     Covariance
• Common distribution functions:
  Beta distribution and the beta function,      Binomial distribution,      Chi-square distribution and chi-square statistic,      F-distribution,      Gaussian (normal) distribution,      Logistic (sech squared) distribution,      Log-normal distribution,      Lorentzian distribution,      Pareto distribution,      Poisson distribution,      Student's t distribution,      P value     and     Order statistic medians
• Extreme distribution functions:
  Type 1 extreme value distributions [Gumbel],      Type 2 extreme value distributions [Fréchet],     Type 3 extreme value distributions:      Weibull distribution      Exponential distribution     Rayleigh distribution
• Gamma and Erlang Distributions and Factorials:
  Gamma distribution and the gamma function,      Erlang distribution and Erlang B and C Equations,      Engset Equation,      Factorials
• Error Function:
  Error function
• Information Entropy:
  Shannon entropy,    Rényi entropy,    Tsallis entropy,    a generalised entropy
• Histograms:
  Histograms

• Constructors,   Enter the weights,    Weighting factor options,    Effective sample number,    Denominator options
• Arithmetic means,   geometric means,   harmonic means,   generalised means (power means),   interquartile means,   root mean square,   median,   subtract the arithmetic mean from an array

• Summary table of methods
• Details of methods
• Last update of the source code: 9 April 2015
• Home Page of Michael Thomas Flanagan's Java Scientific Library
• Other classes, in this library, used by this class

• PsRandom - generation of pseudo-random numbers
• ArrayMaths - mathematical transformations of one dimensional arrays
• Regression - regression procedures
• ErrorProp - error propagation

CONSTRUCTORS

• Creates an instance of Stat.
• The transferred array, aa, may be of type Vector<Object>, ArrayList<Object>, Object[ ], double[ ], Double[ ], float[ ], Float[ ], long[ ], Long[ ], int[ ], Integer[ ], short[ ], Short[ ], byte[ ], Byte[ ], BigDecimal[ ], BigInteger[ ], Complex[ ] or Phasor[ ].
  
• If the array is entered as Vector<Object> ArrayList<Object> or Object[] the individual elements may be of mixed type. The types accepted: Double, Float, Long, Integer, Short, Byte, BigDecimal, BigInteger, Complex or Phasor.
• All elements are converted to the same type according to the following rules:
  • If a Complex or Phasor are present all are converted to Complex
  • If a BigDecimal or BigInteger are present and no Complex or Phasor are present all are converted to BigDecimal
  • Otherwise all are converted to double
  A record of the original types is stored and may be accessed by the originalArrayTypes() method.

ENTER AN ARRAY OF WEIGHTS

EFFECTIVE SAMPLE NUMBER (EFFECTIVE BASE)
Instance methods
Choosing to use the true sample number, n
public void useTrueN()
Usage:                      st.useTrueN();
Sets the sample number option to the use of the true sample number, n, e.g.

The default value is to use the default value nEff where

unless this has been reset by the static method, useStaticEffectiveN() (see below). The option set by the static methods below applies to all instances created within the same application unless this or the following instance method is called. The instance methods of setting the sample number do not alter the static setting of the option.

Choosing to use the effective sample number, n
public void useEffectiveN()
Usage:                      st.useEffectiveN();
Sets the sample number option to the use of the effective sample number, nEff,

e.g. the variance will now be calculated as

The effective sampmple number, nEff, is the default value and this method need only be called if the above method (set to n) or the static method, useStaticTrueN(), has already been called and a reset to nEff is required. The option set by the static methods below applies to all instances created within the same application unless this or the above instance method is called. The instance methods of setting the sample number do not alter the static setting of the option.

Static methods
Choosing to use the true sample number, n
public void setStaticTrueN()
Usage:                      Stat.setStaticTrueN();
Sets the sample number option to the use of the true sample number, n,, e.g.

The default option is to use the default value nEff where

The static methods for setting the sample number also set the default option for all instatiations within the same application. Instance resetting methods (above) may be called to reset the option for an individual instance.

Choosing to use the effective sample number, nEff
public void useStaticEffectiveN()
Usage:                      Stat.useStaticEffectiveN();
Sets the sample number option to the use of the effective sample number, nEff,

e.g. the variance will now be calculated as

The default value is nEff. The static methods for setting the sample number also set the default option for all instatiations within the same application. Instance resetting methods (above) may be called to reset the option for an individual instance.

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