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Sqlite3Stats

Injecting StatsBase functions into any SQLite database in Julia.

In Short

Makes it possible to call

select MEDIAN(fieldname) from tablename

in Julia where median is defined in Julia and related packages and the function is injected to use within SQLite. Database file is not modified.

Installation

julia> using Pkg
julia> Pkg.add("Sqlite3Stats")

Simple use

using SQLite
using Sqlite3Stats 
using DataFrames 

# Any SQLite database
# In our case, it is dbfile.db
db = SQLite.DB("dbfile.db")

# Injecting functions 
Sqlite3Stats.register_functions(db)

Registered Functions and Examples

using SQLite
using Sqlite3Stats 
using DataFrames 

db = SQLite.DB("dbfile.db")

# Injecting functions 
Sqlite3Stats.register_functions(db)

# 1st Quartile 
result = DBInterface.execute(db, "select Q1(num) from table") |> DataFrame 

# 2st Quartile 
result = DBInterface.execute(db, "select Q2(num) from table") |> DataFrame 

# Median (Equals to Q2) 
result = DBInterface.execute(db, "select MEDIAN(num) from table") |> DataFrame 

# 3rd Quartile 
result = DBInterface.execute(db, "select Q3(num) from table") |> DataFrame 

# QUANTILE
result = DBInterface.execute(db, "select QUANTILE(num, 0.25) from table") |> DataFrame 
result = DBInterface.execute(db, "select QUANTILE(num, 0.50) from table") |> DataFrame 
result = DBInterface.execute(db, "select QUANTILE(num, 0.75) from table") |> DataFrame 


# Covariance 
result = DBInterface.execute(db, "select COV(num, other) from table") |> DataFrame 

# Pearson Correlation 
result = DBInterface.execute(db, "select COR(num, other) from table") |> DataFrame 

# Spearman Correlation
result = DBInterface.execute(db, "select SPEARMANCOR(num, other) from table") |> DataFrame 

# Kendall Correlation
result = DBInterface.execute(db, "select KENDALLCOR(num, other) from table") |> DataFrame 

# Median Absolute Deviations 
result = DBInterface.execute(db, "select MAD(num) from table") |> DataFrame 

# Inter-Quartile Range
result = DBInterface.execute(db, "select IQR(num) from table") |> DataFrame 

# Skewness 
result = DBInterface.execute(db, "select SKEWNESS(num) from table") |> DataFrame 

# Kurtosis 
result = DBInterface.execute(db, "select KURTOSIS(num) from table") |> DataFrame 

# Geometric Mean
result = DBInterface.execute(db, "select GEOMEAN(num) from table") |> DataFrame 

# Harmonic Mean
result = DBInterface.execute(db, "select HARMMEAN(num) from table") |> DataFrame 

# Maximum absolute deviations
result = DBInterface.execute(db, "select MAXAD(num) from table") |> DataFrame 

# Mean absolute deviations
result = DBInterface.execute(db, "select MEANAD(num) from table") |> DataFrame 

# Mean squared deviations
result = DBInterface.execute(db, "select MSD(num) from table") |> DataFrame 

# Mode
result = DBInterface.execute(db, "select MODE(num) from table") |> DataFrame 

# WMEAN for weighted mean
result = DBInterface.execute(db, "select WMEAN(num, weights) from table") |> DataFrame 

# WMEDIAN for weighted mean
result = DBInterface.execute(db, "select WMEDIAN(num, weights) from table") |> DataFrame 

# Entropy
result = DBInterface.execute(db, "select ENTROPY(probs) from table") |> DataFrame 

# Slope (a) of linear regression y = b + ax
result = DBInterface.execute(db, "select LINSLOPE(x, y) from table") |> DataFrame 

# Intercept (b) of linear regression y = b + ax
result = DBInterface.execute(db, "select LININTERCEPT(x, y) from table") |> DataFrame

Well-known Probability Related Functions

This family of functions implement QXXX(), PXXX(), and RXXX() for a probability density or mass function XXX. Q for quantile, p for propability or cdf value, R for random number.

QNORM(p, mean, stddev) returns the quantile value $q$

whereas

PNORM(q, mean, stddev) returns $p$ using the equation

$$ \int_{-\infty}^{q} f(x; \mu, \sigma)dx = p $$

and RNORM(mean, stddev) draws a random number from a Normal distribution with mean mean ( $\mu$ ) and standard deviation stddev ( $\sigma$ ) which is defined as

$$ f(x; \mu, \sigma) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2} (\frac{x-\mu}{\sigma})^2} $$

and $-\infty < x < \infty$.

# Quantile of Normal Distribution with mean 0 and standard deviation 1
result = DBInterface.execute(db, "select QNORM(0.025, 0.0, 1.0) from table") |> DataFrame 

# Probability of Normal Distribution with mean 0 and standard deviation 1
result = DBInterface.execute(db, "select PNORM(-1.96, 0.0, 1.0) from table") |> DataFrame 

# Random number drawn from a Normal Distribution with mean * and standard deviation 1
result = DBInterface.execute(db, "select RNORM(0.0, 1.0) from table") |> DataFrame

Other functions for distributions

Note that Q, P, and R prefix correspond to Quantile, CDF (Probability), and Random (number), respectively.

  • QT(x, dof), PT(x, dof), RT(dof) for Student-T Distribution
  • QCHISQ(x, dof), PCHISQ(x, dof), RCHISQ(dof) for ChiSquare Distribution
  • QF(x, dof1, dof2), PF(x, dof1, dof2), RF(dof1, dof2) for F Distribution
  • QPOIS(x, lambda),RPOIS(x, lambda), RPOIS(lambda) for Poisson Distribution
  • QBINOM(x, n, p), PBINOM(x, n, p), RBINOM(n, p) for Binomial Distribution
  • QUNIF(x, a, b), PUNIF(x, a, b), RUNIF(a, b) for Uniform Distribution
  • QEXP(x, theta), PEXP(x, theta), REXP(theta) for Exponential Distribution
  • QBETA(x, alpha, beta), PGAMMA(x, alpha, beta), RGAMMA(alpha, beta) for Beta Distribution
  • QCAUCHY(x, location, scale), PCAUCHY(x, location, scale), RCAUCHY(location, scale) for Cauchy Distribution
  • QGAMMA(x, alpha, theta), PGAMMA(x, alpha, theta), RGAMMA(alpha, theta) for Gamma Distribution
  • QFRECHET(x, alpha), PFRECHET(x, alpha), RFRECHET(alpha) for Frechet Distribution
  • QPARETO(x, alpha, theta), PPARETO(x, alpha, theta), RPARETO(alpha, theta) for Pareto Distribution
  • QWEIBULL(x, alpha, theta), PWEIBULL(x, alpha, theta), RWEIBULL(alpha, theta) for Weibull Distribution

Hypothesis Tests

  • JB(x) for Jarque-Bera Normality Test (returns the p-value)

The Logic

The package mainly uses the register function. For example, a single variable function MEDIAN is registered as

SQLite.register(db, [], 
        (x,y) -> vcat(x, y), 
        x -> StatsBase.quantile(x, 0.50), 
        name = "MEDIAN")

whereas, the two-variable function COR is registered as

SQLite.register(db, Array{Float64, 2}(undef, (0, 2)), 
        (x, a, b) -> vcat(x, [a, b]'), 
        x -> StatsBase.cor(x[:,1], x[:,2]), 
        name = "COR", nargs = 2)

for Pearson's correlation coefficient.