Class that contains certain functions related to statistics, such as the student's t distribution.
Definition at line 27 of file Statistics.h.
| float64_t confidence_intervals_mean | ( | SGVector< float64_t > | values, | |
| float64_t | alpha, | |||
| float64_t & | conf_int_low, | |||
| float64_t & | conf_int_up | |||
| ) | [static] |
Calculates the sample mean of a given set of samples and also computes the confidence interval for the actual mean for a given p-value, asuming that the actual variance and mean are unknown (These are estimated by the samples)
Only for normally distributed data
| values | vector of values that are used for calculations | |
| alpha | actual mean lies in confidence interval with (1-alpha)*100% | |
| conf_int_low | lower confidence interval border is written here | |
| conf_int_up | upper confidence interval border is written here |
Definition at line 52 of file Statistics.cpp.
| virtual const char* get_name | ( | ) | const [virtual] |
| float64_t ibetaf_incomplete_beta_fe | ( | float64_t | a, | |
| float64_t | b, | |||
| float64_t | x, | |||
| float64_t | big, | |||
| float64_t | biginv | |||
| ) | [static, protected] |
Continued fraction expansion #1 for incomplete beta integral
Taken from ALGLIB under GPL2+
Definition at line 435 of file Statistics.cpp.
| float64_t ibetaf_incomplete_beta_fe2 | ( | float64_t | a, | |
| float64_t | b, | |||
| float64_t | x, | |||
| float64_t | big, | |||
| float64_t | biginv | |||
| ) | [static, protected] |
Continued fraction expansion #2 for incomplete beta integral
Taken from ALGLIB under GPL2+
Definition at line 331 of file Statistics.cpp.
| float64_t ibetaf_incomplete_beta_ps | ( | float64_t | a, | |
| float64_t | b, | |||
| float64_t | x, | |||
| float64_t | maxgam | |||
| ) | [static, protected] |
Power series for incomplete beta integral. Use when b*x is small and x not too close to 1.
Taken from ALGLIB under GPL2+
Definition at line 278 of file Statistics.cpp.
Incomplete beta integral Returns incomplete beta integral of the arguments, evaluated from zero to x. The domain of definition is 0 <= x <= 1. In this implementation a and b are restricted to positive values. The integral is evaluated by a continued fraction expansion or, when b*x is small, by a power series.
Taken from ALGLIB under GPL2+
Definition at line 154 of file Statistics.cpp.
Inverse of imcomplete beta integral Given y, the function finds x such that inverse_incomplete_beta(a, b, x) = y . The routine performs interval halving or Newton iterations to find the root of inverse_incomplete_beta(a, b, x)-y=0.
Taken from ALGLIB under GPL2+
Definition at line 581 of file Statistics.cpp.
Inverse of Normal distribution function Returns the argument, x, for which the area under the Gaussian probability density function (integrated from minus infinity to x) is equal to y.
For small arguments 0 < y < exp(-2), the program computes z=sqrt(-2.0*log(y)) then the approximation is x=z-log(z)/z-(1/z)P(1/z)/Q(1/z). There are two rational functions P/Q, one for 0 < y < exp(-32) and the other for y up to exp(-2). For larger arguments, w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
Taken from ALGLIB under GPL2+
Definition at line 1029 of file Statistics.cpp.
Functional inverse of Student's t distribution Given probability p, finds the argument t such that stdtr(k,t) is equal to p.
Taken from ALGLIB under GPL2+
Definition at line 537 of file Statistics.cpp.
Calculates mean of given values
| values | vector of values |
Definition at line 21 of file Statistics.cpp.
Calculates standard deviation of given values
| values | vector of values |
Definition at line 47 of file Statistics.cpp.
Student's t distribution Computes the integral from minus infinity to t of the Student For t < -2, this is the method of computation. For higher t, a direct method is derived from integration by parts. Since the function is symmetric about t=0, the area under the right tail of the density is found by calling the function with -t instead of t. Taken from ALGLIB under GPL2+
| k | degrees of freedom | |
| t | integral is computed from minus infinity to t |
Definition at line 79 of file Statistics.cpp.
Calculates variance of given values
| values | vector of values |
Definition at line 33 of file Statistics.cpp.
