This topic describes the syntax of mathematical statistics functions. This topic also provides examples on how to use the functions.
Log Service supports the following mathematical statistics functions.
Category | Function | Syntax | Description |
---|---|---|---|
Correlation functions | corr function | corr(x, y) | Returns the coefficient of correlation between x and y. The return value is in the range of [0,1]. |
Variance and standard deviation functions | covar_pop function | covar_pop(x, y) | Returns the population covariance of x and y. |
covar_samp function | covar_samp(x, y) | Returns the sample covariance of x and y. | |
stddev function | stddev(x) | Returns the sample standard deviation of x. This function is equivalent to the stddev_samp function. | |
stddev_samp function | stddev_samp(x) | Returns the sample standard deviation of x. | |
stddev_pop function | stddev_pop(x) | Returns the population standard deviation of x. | |
variance function | variance(x) | Returns the sample variance of x. This function is equivalent to the var_samp function. | |
var_samp function | var_samp(x) | Returns the sample variance of x. | |
var_pop function | var_pop(x) | Returns the population variance of x. | |
Linear regression functions | regr_intercept function | regr_intercept(y, x) | Returns the y-intercept of the line for the linear equation that is determined by the (x,y) pair. |
regr_slope function | regr_slope(y, x) | Returns the slope of the line for the linear equation that is determined by the (x,y) pair. | |
Cumulative distribution functions (CDFs) | beta_cdf function | beta_cdf(α, β, v) | Returns a value for the beta distribution. The function uses the following formula: P(N <= v; α, β) where α and β are parameters for the beta CDF. |
binomial_cdf function | binomial_cdf(x, y, v) | Returns a value for the binomial distribution. The function uses the following formula: P(N <= v; x, y) where x indicates the number of trials, and y indicates the probability of success (POS) of a trial. | |
cauchy_cdf function | cauchy_cdf(x, y, v) | Returns a value for the Cauchy distribution. The function uses the following formula: P(N <= v; x, y) where x is the location parameter indicating the peak of the distribution, and y is the scale parameter. | |
chi_squared_cdf function | chi_squared_cdf(k, v) | Returns a value for the chi-square distribution. The function uses the following formula: P(N <= v; k) where k indicates the degree of freedom. | |
inverse_beta_cdf function | inverse_beta_cdf(α, β, p) | Returns a value for the inverse of the beta distribution. p indicates the result of the beta CDF, which uses the P(N <= v; α, β) formula. The inverse inverse_beta_cdf function calculates v. | |
inverse_binomial_cdf function | inverse_binomial_cdf(x, y, p) | Returns a value for the inverse of the binomial distribution. p indicates the result of the binomial CDF, which uses the P(N <= v; x, y) formula. The inverse inverse_binomial_cdf function calculates v. | |
inverse_cauchy_cdf function | inverse_cauchy_cdf(x, y, p) | Returns a value for the inverse of the Cauchy distribution. p indicates the result of the Cauchy CDF, which uses the P(N <= v; x, y) formula. The inverse inverse_cauchy_cdf function calculates v. | |
inverse_chi_squared_cdf function | inverse_chi_squared_cdf(k, p) | Returns a value for the inverse of the chi-square distribution. p indicates the result of the chi-square CDF, which uses the P(N <= v; k) formula. The inverse inverse_chi_squared_cdf function calculates v. | |
inverse_laplace_cdf function | inverse_laplace_cdf(μ, b, p) | Returns a value for the inverse of the Laplace distribution. p indicates the result of the Laplace CDF, which uses the P(N <= v; μ, b) formula. The inverse inverse_laplace_cdf function calculates v. | |
inverse_normal_cdf function | inverse_normal_cdf(x, y, p) | Returns a value for the inverse of the normal distribution. p indicates the result of the normal CDF, which uses the P(N < v; x, y) formula. The inverse inverse_normal_cdf function calculates v. | |
inverse_poisson_cdf function | inverse_poisson_cdf(x, y, p) | Returns a value for the inverse of the Poisson distribution. p indicates the result of the Poisson CDF, which uses the P(N <= v; λ) formula. The inverse inverse_poisson_cdf function calculates v. | |
inverse_weibull_cdf function | inverse_weibull_cdf(x, y, p) | Returns a value for the inverse of the Weibull distribution. p indicates the result of the Weibull CDF, which uses the P(N <= v; x, y) formula. The inverse inverse_weibull_cdf function calculates v. | |
laplace_cdf function | laplace_cdf( μ, b, v) | Returns a value for the Laplace distribution. The function uses the following formula: P(N <= v; μ, b) where μ is the location parameter, and b is the scale parameter. | |
normal_cdf function | normal_cdf(x, y, v) | Returns a value for the normal distribution. The function uses the following formula: P(N < v; x, y) where x indicates the mean value for the normal distribution, and y indicates the standard deviation for the normal distribution. | |
poisson_cdf function | poisson_cdf( λ, v) | Returns a value for the Poisson distribution. The function uses the following formula: P(N <= v; λ) where λ indicates the average probability of random events. | |
weibull_cdf function | weibull_cdf(x, y, v) | Returns a value for the Weibull distribution. The function uses the following formula: P(N <= v; x, y) where x is the scale parameter, and y is the shape parameter. |
corr function
The corr function returns the coefficient of correlation between x and y. A larger return value indicates a higher correlation.
Syntax
corr(x, y)
Parameters
Parameter | Description |
---|---|
x | The value of this parameter is of the double type. |
y | The value of this parameter is of the double type. |
Response
The double type. The return value is in the range of [0,1].
Examples
Calculate the coefficient of correlation between the values of the request_length and request_time fields.
- Query statement
* | SELECT corr(request_length,request_time)
- Query and analysis results
covar_pop function
The covar_pop function returns the population covariance of x and y.
Syntax
covar_pop(x, y)
Parameters
Parameter | Description |
---|---|
x | The value of this parameter is of the double type. |
y | The value of this parameter is of the double type. |
Response
The double type.
Examples
Calculate the population covariance of pretax profits and pretax turnovers in each minute.
- Query statement
*| SELECT covar_pop(PretaxGrossAmount, PretaxAmount) AS "Population covariance", time_series(__time__, '1m', '%H:%i:%s', '0') AS time GROUP BY time
- Query and analysis results
covar_samp function
The covar_samp function returns the sample covariance of x and y.
Syntax
covar_samp(x, y)
Parameters
Parameter | Description |
---|---|
x | The value of this parameter is of the double type. |
y | The value of this parameter is of the double type. |
Response
The double type.
Examples
Calculate the sample covariance of pretax profits and pretax turnovers in each minute.
- Query statement
*| SELECT covar_samp(PretaxGrossAmount, PretaxAmount) AS "Sample covariance", time_series(__time__, '1m', '%H:%i:%s', '0') AS time GROUP BY time
- Query and analysis results
stddev function
The stddev function returns the sample standard deviation of x. This function is equivalent to the stddev_samp function.
Syntax
stddev(x)
Parameters
Parameter | Description |
---|---|
x | The value of this parameter is of the double or bigint type. |
Response
The double type.
Examples
Calculate the sample standard deviation and population standard deviation of pretax incomes and display the calculated values in a line chart.
- Query statement
* | SELECT stddev(PretaxGrossAmount) as "Sample standard deviation", stddev_pop(PretaxGrossAmount) as "Population standard deviation", time_series(__time__, '1m', '%H:%i:%s', '0') AS time GROUP BY time
- Query and analysis results
stddev_samp function
The stddev_samp function returns the sample standard deviation of x.
Syntax
stddev_samp(x)
Parameters
Parameter | Description |
---|---|
x | The value of this parameter is of the double or bigint type. |
Response
The double type.
Examples
Calculate the sample standard deviation and population standard deviation of pretax incomes and display the calculated values in a line chart.
- Query statement
* | SELECT stddev_samp(PretaxGrossAmount) as "Sample standard deviation", stddev_pop(PretaxGrossAmount) as "Population standard deviation", time_series(__time__, '1m', '%H:%i:%s', '0') AS time GROUP BY time
- Query and analysis results
stddev_pop function
The stddev_pop function returns the population standard deviation of x.
Syntax
stddev_pop(x)
Parameters
Parameter | Description |
---|---|
x | The value of this parameter is of the double or bigint type. |
Response
The double type.
Examples
Calculate the sample standard deviation and population standard deviation of pretax incomes and display the calculated values in a line chart.
- Query statement
* | SELECT stddev(PretaxGrossAmount) as "Sample standard deviation", stddev_pop(PretaxGrossAmount) as "Population standard deviation", time_series(__time__, '1m', '%H:%i:%s', '0') AS time GROUP BY time
- Query and analysis results
variance function
The variance function returns the sample variance of x. This function is equivalent to the var_samp function.
Syntax
variance(x)
Parameters
Parameter | Description |
---|---|
x | The value of this parameter is of the double or bigint type. |
Response
The double type.
Examples
Calculate the sample variance and population variance of pretax incomes and display the calculated values in a line chart.
- Query statement
* | SELECT variance(PretaxGrossAmount) as "Sample variance", var_pop(PretaxGrossAmount) as "Population variance", time_series(__time__, '1m', '%H:%i:%s', '0') as time GROUP BY time
- Query and analysis results
var_samp function
The var_samp function returns the sample variance of x.
Syntax
var_samp(x)
Parameters
Parameter | Description |
---|---|
x | The value of this parameter is of the double or bigint type. |
Response
The double type.
Examples
Calculate the sample variance and population variance of pretax incomes and display the calculated values in a line chart.
- Query statement
* | SELECT var_samp(PretaxGrossAmount) as "Sample variance", var_pop(PretaxGrossAmount) as "Population variance", time_series(__time__, '1m', '%H:%i:%s', '0') as time GROUP BY time
- Query and analysis results
var_pop function
The var_pop function returns the population variance of x.
Syntax
var_pop(x)
Parameters
Parameter | Description |
---|---|
x | The value of this parameter is of the double or bigint type. |
Response
The double type.
Examples
Calculate the sample variance and population variance of pretax incomes and display the calculated values in a line chart.
- Query statement
* | SELECT variance(PretaxGrossAmount) as "Sample variance", var_pop(PretaxGrossAmount) as "Population variance", time_series(__time__, '1m', '%H:%i:%s', '0') as time GROUP BY time
- Query and analysis results
regr_intercept function
The regr_intercept function returns the y-intercept of the line for the linear equation that is determined by the (x,y)
pair. x is the dependent value. y is the independent value.
Syntax
regr_intercept(y, x)
Parameters
Parameter | Description |
---|---|
y | The value of this parameter is of the double type. |
x | The value of this parameter is of the double type. |
Response
The double type.
Examples
Calculate the y-intercept of the line for the linear equation that is determined by the values of the request_time and request_length fields.
- Query statement
* | SELECT regr_intercept(request_length,request_time)
- Query and analysis results
regr_slope function
The regr_slope function returns the slope of the line for the linear equation that is determined by the (x,y)
pair. x is the dependent value. y is the independent value.
Syntax
regr_slope(y, x)
Parameters
Parameter | Description |
---|---|
y | The value of this parameter is of the double type. |
x | The value of this parameter is of the double type. |
Response
The double type.
Examples
Calculate the slope of the line for the linear equation that is determined by the values of the request_time and request_length fields.
- Query statement
* | SELECT regr_slope(request_length,request_time)
- Query and analysis results
beta_cdf function
The beta_cdf function returns a value for the beta distribution.
Syntax
beta_cdf(α, β, v)
Parameters
Parameter | Description |
---|---|
α | The parameter for the beta CDF. The value of this parameter is of the double type. The value is greater than 0. |
β | The parameter for the beta CDF. The value of this parameter is of the double type. The value is greater than 0. |
v | The input parameter for the beta CDF. The value of this parameter is of the double type. Valid values: [0,1]. |
Response
The double type.
Examples
- Query statement
* | SELECT beta_cdf(0.1, 0.5, 0.7)
- Query and analysis results
binomial_cdf function
The binomial_cdf function returns a value for the binomial distribution.
Syntax
binomial_cdf(x, y, v)
Parameters
Parameter | Description |
---|---|
x | The number of trials. The value of this parameter is of the integer type. The value is greater than 0. |
y | The POS of a trial. The value of this parameter is of the double type. Valid values: [0,1]. |
v | The input parameter for the binomial CDF. The value of this parameter is of the integer type. |
Response
The double type.
Examples
- Query statement
* | select binomial_cdf(10, 0.1, 1)
- Query and analysis results
cauchy_cdf function
The cauchy_cdf function returns a value for the Cauchy distribution.
Syntax
cauchy_cdf(x, y, v)
Parameters
Parameter | Description |
---|---|
x | The location parameter that indicates the peak of the distribution. The value of this parameter is of the double type. |
y | The scale parameter. The value of this parameter is of the double type. The value is greater than 0. |
v | The input parameter for the Cauchy CDF. The value of this parameter is of the double type. |
Response
The double type.
Examples
- Query statement
* | select cauchy_cdf(-10, 5, -12)
- Query and analysis results
chi_squared_cdf function
The chi_squared_cdf function returns a value for the chi-square distribution.
Syntax
chi_squared_cdf(k, v)
Parameters
Parameter | Description |
---|---|
k | The degree of freedom. The value of this parameter is of the double type. The value is greater than 0. |
v | The input parameter of the chi-square CDF. The value of this parameter is of the double type. The value is greater than or equal to 0. |
Response
The double type.
Examples
- Query statement
* | select chi_squared_cdf(3, 10)
- Query and analysis results
inverse_beta_cdf function
The inverse_beta_cdf function returns a value for the inverse of the beta distribution.
Syntax
inverse_beta_cdf(α, β, p)
Parameters
Parameter | Description |
---|---|
α | The parameter for the beta CDF. The value of this parameter is of the double type. The value is greater than 0. |
β | The parameter for the beta CDF. The value of this parameter is of the double type. The value is greater than 0. |
p | The input parameter for the inverse of the beta CDF. The value of this parameter is of the double type. Valid values: [0,1]. |
Response
The double type.
Examples
- Query statement
* | select inverse_beta_cdf(0.1, 0.5, 0.8926585878364057)
- Query and analysis results
inverse_binomial_cdf function
The inverse_binomial_cdf function returns a value for the inverse of the binomial distribution.
Syntax
inverse_binomial_cdf(x, y, p)
Parameters
Parameter | Description |
---|---|
x | The number of trials. The value of this parameter is of the integer type. The value is greater than 0. |
y | The POS of a trial. The value of this parameter is of the double type. Valid values: [0,1]. |
p | The input parameter for the inverse of the binomial CDF. The value of this parameter is of the double type. Valid values: [0,1]. |
Response
The integer type.
Examples
- Query statement
* | select inverse_binomial_cdf(10, 0.1, 0.7360989291000001)
- Query and analysis results
inverse_cauchy_cdf function
The inverse_cauchy_cdf function returns a value for the inverse of the Cauchy distribution.
Syntax
inverse_cauchy_cdf(x, y, p)
Parameters
Parameter | Description |
---|---|
x | The location parameter that indicates the peak of the distribution. The value of this parameter is of the double type. |
y | The scale parameter. The value of this parameter is of the double type. The value is greater than 0. |
p | The input parameter for the inverse of the Cauchy CDF. The value of this parameter is of the double type. Valid values: [0,1]. |
Response
The double type.
Examples
- Query statement
* | select inverse_cauchy_cdf(-10, 5, 0.3788810584091566)
- Query and analysis results
inverse_chi_squared_cdf function
The inverse_chi_squared_cdf function returns a value for the inverse of the chi-square distribution.
Syntax
chi_squared_cdf(k, p)
Parameters
Parameter | Description |
---|---|
k | The degree of freedom. The value of this parameter is of the double type. The value is greater than 0. |
p | The input parameter for the inverse of the chi-square CDF. The value of this parameter is of the double type. Valid values: [0,1]. |
Response
The double type.
Examples
- Query statement
* | select inverse_chi_squared_cdf(3, 0.9814338645369567)
- Query and analysis results
inverse_laplace_cdf function
The inverse_laplace_cdf function returns a value for the inverse of the Laplace distribution.
Syntax
inverse_laplace_cdf(μ, b, p)
Parameters
Parameter | Description |
---|---|
μ | The location parameter for the Laplace CDF. The value of this parameter is of the double type. |
b | The scale parameter for the Laplace CDF. The value of this parameter is of the double type. The value is greater than 0. |
p | The input parameter for the inverse of the Laplace CDF. The value of this parameter is of the double type. Valid values: [0,1]. |
Response
The double type.
Examples
- Query statement
* | select inverse_laplace_cdf(11, 0.5, 0.18393972058572118)
- Query and analysis results
inverse_normal_cdf function
The inverse_normal_cdf function returns a value for the inverse of the normal distribution.
Syntax
inverse_normal_cdf(x, y, p)
Parameters
Parameter | Description |
---|---|
x | The mean value for the normal distribution. The value of this parameter is of the double type. |
y | The standard deviation for the normal distribution. The value of this parameter is of the double type. The value is greater than 0. |
p | The input parameter for the inverse of the normal CDF. The value of this parameter is of the double type. Valid values: (0,1). |
Response
The double type.
Examples
- Query statement
* | select inverse_normal_cdf(85, 10, 0.06680720126885803)
- Query and analysis results
inverse_poisson_cdf function
The inverse_poisson_cdf function returns a value for the inverse of the Poisson distribution.
Syntax
inverse_poisson_cdf(λ, p)
Parameters
Parameter | Description |
---|---|
λ | The average probability of random events. |
p | The input parameter for the inverse of the Poisson CDF. The value of this parameter is of the double type. Valid values: [0,1]. |
Response
The integer type.
Examples
- Query statement
* | select inverse_poisson_cdf(0.1, 0.9953211598395556)
- Query and analysis results
inverse_weibull_cdf function
The inverse_weibull_cdf function returns a value for the inverse of the Weibull distribution.
Syntax
inverse_weibull_cdf(x, y, p)
Parameters
Parameter | Description |
---|---|
x | The scale parameter for the Weibull CDF. The value of this parameter is of the double type. The value is greater than 0. |
y | The shape parameter for the Weibull CDF. The value of this parameter is of the double type. The value is greater than 0. |
p | The input parameter for the inverse of the Weibull CDF. The value of this parameter is of the double type. Valid values: [0,1]. |
Response
The double type.
Examples
- Query statement
* | select inverse_weibull_cdf(1, 5, 0.3296799539643607)
- Query and analysis results
laplace_cdf function
The laplace_cdf function returns a value for the Laplace distribution.
Syntax
laplace_cdf(μ, b, v)
Parameters
Parameter | Description |
---|---|
μ | The location parameter for the Laplace CDF. The value of this parameter is of the double type. |
b | The scale parameter for the Laplace CDF. The value of this parameter is of the double type. The value is greater than 0. |
v | The input parameter for the Laplace CDF. The value of this parameter is of the double type. |
Response
The double type.
Examples
- Query statement
* | select laplace_cdf(11, 0.5, 10.5)
- Query and analysis results
normal_cdf function
The normal_cdf function returns a value for the normal distribution.
Syntax
normal_cdf(x, y, v)
Parameters
Parameter | Description |
---|---|
x | The mean value for the normal distribution. The value of this parameter is of the double type. |
y | The standard deviation for the normal distribution. The value of this parameter is of the double type. The value is greater than 0. |
v | The input parameter for the normal CDF. The value of this parameter is of the double type. |
Response
The double type.
Examples
- Query statement
* | select normal_cdf(85, 10, 70)
- Query and analysis results
poisson_cdf function
The poisson_cdf function returns a value for the Poisson distribution.
Syntax
poisson_cdf(λ, v)
Parameters
Parameter | Description |
---|---|
λ | The average probability of random events. |
v | The input parameter for the Poisson CDF. The value of this parameter is of the integer type. The value is greater than or equal to 0. |
Response
The double type.
Examples
- Query statement
* | select poisson_cdf(0.1, 1)
- Query and analysis results
weibull_cdf function
The weibull_cdf function returns a value for the Weibull distribution.
Syntax
weibull_cdf(x, y, v)
Parameters
Parameter | Description |
---|---|
x | The scale parameter for the Weibull CDF. The value of this parameter is of the double type. The value is greater than 0. |
y | The shape parameter for the Weibull CDF. The value of this parameter is of the double type. The value is greater than 0. |
v | The input parameter for the Weibull CDF. The value of this parameter is of the double type. |
Response
Examples
- Query statement
* | select weibull_cdf(1, 5, 2)
- Query and analysis results