Package Cl-Mathstats uses the packages Common-Lisp, Metabang.Cl-Containers and Metabang.Utilities. It is also known as Metabang.Math. It has 784 total symbols and 106 external ones.
| data-error | |
|---|---|
| enormous-contingency-table | |
| insufficient-data | |
| no-data | |
| not-binary-variables | |
| unmatched-sequences | |
| zero-standard-deviation | |
| zero-variance |
| *continous-data-window-divisor* | |
|---|---|
| *continuous-variable-uniqueness-factor* | |
| *create-statistical-objects* | |
| *gaussian-cdf-signals-zero-standard-deviation-error* | |
| *temporary-table* | |
| *temporary-vector* | |
| *way-too-big-contingency-table-dimension* |
| +0degrees+ | |
|---|---|
| +10degrees+ | |
| +120degrees+ | |
| +135degrees+ | |
| +150degrees+ | |
| +15degrees+ | |
| +180degrees+ | |
| +210degrees+ | |
| +225degrees+ | |
| +240degrees+ | |
| +270degrees+ | |
| +300degrees+ | |
| +30degrees+ | |
| +315degrees+ | |
| +330degrees+ | |
| +360degrees+ | |
| +45degrees+ | |
| +5degrees+ | |
| +60degrees+ | |
| +90degrees+ | |
| +e+ | |
| +log-pi+ | |
| +sqrt-pi+ | |
| 2fpi | The constant 2*pi, in single-float format. Using this constant avoid run-time double-float conta... |
| fpi | The constant pi, in single-float format. Using this constant avoid run-time double-float contagi... |
| 1-or-2d-arrayp | |
|---|---|
| anova-one-way-groups | Performs a one-way analysis of variance (ANOVA) on the `data,' which should be a sequence of sequ... |
| anova-one-way-variables | ANOVA-ONE-WAY-VARIABLES (IV DV &OPTIONAL (SCHEFFE-TESTS-P T) CONFIDENCE-... |
| anova-one-way-variables-internal | See ANOVA-ONE-WAY-VARIABLES |
| anova-two-way-groups | Calculates the analysis of variance when there are two factors that may affect the dependent vari... |
| anova-two-way-variables | ANOVA-TWO-WAY-VARIABLES (DV IV1 IV2) Calculates the analysis of variance when there are two facto... |
| anova-two-way-variables-internal | See ANOVA-TWO-WAY-VARIABLES |
| anova-two-way-variables-unequal-cell-sizes | ANOVA-TWO-WAY-VARIABLES-UNEQUAL-CELL-SIZES (IV1 IV2 DV) Calculates the analysis of variance when ... |
| anova-two-way-variables-unequal-cell-sizes-internal | See ANOVA-TWO-WAY-VARIABLES-UNEQUAL-CELL-SIZES |
| autocorrelation | AUTOCORRELATION (SAMPLE MAX-LAG &OPTIONAL (MIN-LAG 0)) Autocorrelation is merely a cross-correlat... |
| autocorrelation-internal | See AUTOCORRELATION |
| beta | Returns the value of the Beta function, defined in terms of the complete gamma function, G, as: G... |
| beta-incomplete | This function is useful in defining the cumulative distributions for Student's t and the F distri... |
| binomial-cdf | Suppose an event occurs with probability `p' per trial. This function computes the probability o... |
| binomial-cdf-exact | This is an exact but computationally intensive form of the preferred function, `binomial-cdf.' |
| binomial-coefficient | Returns the binomial coefficient, `n' choose `k,' as an integer. The result may not be exactly c... |
| binomial-coefficient-exact | This is an exact but computationally intensive form of the preferred function, `binomial-coeffici... |
| binomial-probability | Returns the probability of `k' successes in `n' trials, where at each trial the probability of su... |
| binomial-probability-exact | This is an exact but computationally intensive form of the preferred function, `binomial-probabil... |
| chi-square-2x2 | Performs a chi-square test for independence of the two variables, `v1' and `v2.' These should be ... |
| chi-square-2x2-counts | Runs a chi-square test for association on a simple 2 x 2 table. If `yates' is nil, the correctio... |
| chi-square-rxc | Performs a chi-square test for independence of the two variables, `v1' and `v2.' These should be ... |
| chi-square-rxc-counts | Calculates the chi-square statistic and corresponding p-value for the given contingency table. T... |
| chi-square-significance | Computes the complement of the cumulative distribution function for a Chi-square random variable ... |
| combination-count | Returns the number of combinations of n elements taken k at a time. Assumes valid input. |
| confidence-interval | CONFIDENCE-INTERVAL NIL NIL |
| confidence-interval-internal | |
| confidence-interval-proportion | CONFIDENCE-INTERVAL-PROPORTION (X N CONFIDENCE) Suppose we have a sample of `n' things and `x' of... |
| confidence-interval-proportion-internal | See CONFIDENCE-INTERVAL-PROPORTION |
| confidence-interval-t | CONFIDENCE-INTERVAL-T (DATA CONFIDENCE) Suppose you have a sample of 10 numbers and you want to c... |
| confidence-interval-t-internal | See CONFIDENCE-INTERVAL-T |
| confidence-interval-t-summaries | This function is just like `confidence-interval-t,' except that instead of its arguments being th... |
| confidence-interval-z | CONFIDENCE-INTERVAL-Z (DATA CONFIDENCE) Suppose you have a sample of 50 numbers and you want to c... |
| confidence-interval-z-internal | See CONFIDENCE-INTERVAL-Z |
| confidence-interval-z-summaries | This function is just like `confidence-interval-z,' except that instead of its arguments being th... |
| correlation | CORRELATION (SAMPLE1 SAMPLE2 &KEY START1 END1 START2 END2) Computes the correlation coefficient o... |
| correlation-from-summaries | Computes the correlation of two variables given summary statistics of the variables. All of thes... |
| correlation-internal | See CORRELATION |
| correlation-matrix | Returns a matrix of all the correlations of all the variables. The dependent variable is row and... |
| covariance | COVARIANCE (SAMPLE1 SAMPLE2 &KEY START1 END1 START2 END2) Computes the covariance of two samples,... |
| covariance-internal | See COVARIANCE |
| cross-correlation | CROSS-CORRELATION (SEQUENCE1 SEQUENCE2 MAX-LAG &OPTIONAL (MIN-LAG 0)) Returns a list of the corre... |
| cross-correlation-internal | See CROSS-CORRELATION |
| d-test | D-TEST (SAMPLE-1 SAMPLE-2 TAILS &KEY (TIMES 1000) (H0MEAN 0)) Two-sample test for difference in m... |
| d-test-internal | See D-TEST |
| data-continuous-p | |
| data-length | DATA-LENGTH (DATA &KEY START END KEY) Returns the number of data values in `data.' Essentially, t... |
| data-length-internal | See DATA-LENGTH |
| degrees->radians | Convert degrees to radians. |
| difference-list | Takes a sequence of numbers and returns a sequence of differences from the mean. Formula: xi = X... |
| div2 | Divide positive fixnum `i' by 2 or a power of 2, yielding an integer result. For example, (div2 3... |
| ensure-float | |
| error-function | Computes the error function, which is typically used to compute areas under the Gaussian probabil... |
| error-function-complement | This function computes the complement of the error function, ``erfc(x),'' defined as 1-erf(x). S... |
| error-function-complement-short-1 | |
| error-function-complement-short-2 | |
| exp2 | 2^n |
| extract-unique-values | A faster version of `remove-duplicates'. Note you cannot specify a :TEST (it is always #'eq). |
| f-measure | Returns the f-measure, the combination of precision and recall based on parameter beta - default ... |
| f-significance | This function occurs in the statistical test of whether two observed samples have the same varian... |
| factorial | Returns the factorial of `n,' which should be a non-negative integer. The result will returned a... |
| factorial-exact | Returns the factorial of `n,' which should be an integer. The result will returned as an integer... |
| factorial-ln | Returns the natural logarithm of n!; `n' should be an integer. The result will be a single-preci... |
| fill-2d-array | |
| find-critical-value | Returns the critical value of some statistic. The function `p-function' should be a unary functi... |
| g-test | Calculates the G-test for a contingency table. The formula for the G-test statistic is 2 * sum[... |
| gamma-incomplete | This is an incomplete gamma function, what Numerical Recipes in C calls ``gammp.'' This function ... |
| gamma-ln | Returns the natural logarithm of the Gamma function evaluated at `x.' Mathematically, the Gamma f... |
| gaussian-cdf | Computes the cumulative distribution function for a Gaussian random variable (defaults: mean=0.0,... |
| gaussian-significance | Computes the significance of `x' in a Gaussian distribution with mean=`mean' (default 0.0) and st... |
| inner-product | Returns the inner product of the two samples, which should be sequences of numbers. The inner pr... |
| interquartile-range | INTERQUARTILE-RANGE (DATA) The interquartile range is similar to the variance of a sample because... |
| interquartile-range-internal | See INTERQUARTILE-RANGE |
| invert-matrix | If matrix is singular returns nil, else returns its inverse. If into-matrix is supplied, inver... |
| invert-matrix-iterate | If matrix is singular returns nil, else returns the inverse of matrix. Uses iterative improvem... |
| lagged-correlation | Returns the correlations of `sequence1' with `sequence2' after shifting `sequence1' by `lag'. Th... |
| linear-regression-brief | Calculates the main statistics of a linear regression: the slope and intercept of the line, the c... |
| linear-regression-brief-summaries | Calculates the main statistics of a linear regression: the slope and intercept of the line, the c... |
| linear-regression-minimal | Calculates the slope and intercept of the regression line. This function takes two equal-length ... |
| linear-regression-minimal-summaries | Calculates the slope and intercept of the regression line. This function differs from `linear-re... |
| linear-regression-verbose | Calculates almost every statistic of a linear regression: the slope and intercept of the line, th... |
| linear-regression-verbose-summaries | Calculates almost every statistic of a linear regression: the slope and intercept of the line, th... |
| linear-scale | Rescales value linearly from the old-min/old-max scale to the new-min/new-max one. |
| list-2d-array | |
| log2 | Log of `n' to base 2. |
| make-3d-table | Collects the `dv' values for each unique combination of an element of `v1' and an element of `v2.... |
| make-contingency-table | Counts each unique combination of an element of `v1' and an element of `v2.' Returns a two-dimens... |
| matrix-addition | |
| matrix-multiply | Does successive multiplications of each element in `args'. If two elements are scalar, then thei... |
| matrix-norm | Returns the norm of matrix. The norm is the maximum over the rows of the sum of the abs of the... |
| matrix-plus-matrix | Adds two matrices together |
| matrix-plus-scalar | Add a scalar value to a matrix |
| matrix-times-matrix | Multiplies two matrices together |
| matrix-times-scalar | Multiply a matrix by a scalar value |
| matrix-times-scalar! | Multiply a matrix by a scalar value |
| matrix-trace | |
| maximum | MAXIMUM (DATA &KEY START END KEY) Returns the element of the sequence `data' whose `key' is maxim... |
| maximum-internal | See MAXIMUM |
| mean | MEAN (DATA &KEY START END KEY) Returns the arithmetic mean of `data,' which should be a sequence.... |
| mean-internal | See MEAN |
| median | MEDIAN (DATA &KEY START END KEY) Returns the median of the subsequence of `data' from `start' to ... |
| median-internal | See MEDIAN |
| minimum | MINIMUM (DATA &KEY START END KEY) Returns the element of the sequence `data' whose `key' is minim... |
| minimum-internal | See MINIMUM |
| mod2 | Find `n' mod a power of 2. |
| mode | MODE (DATA &KEY START END KEY) Returns the most frequent element of `data,' which should be a seq... |
| mode-for-continuous-data | Returns the most frequent element of `data,' which should be a sequence. The algorithm involves ... |
| mode-internal | See MODE |
| multiple-linear-regression-arrays | This is an internal function for the use of the multiple-linear-regression functions. It takes t... |
| multiple-linear-regression-brief | Let m be the number of independent variables, `ivs.' This function returns a vector of length m w... |
| multiple-linear-regression-minimal | Let m be the number of independent variables, `ivs.' This function returns a vector of length m ... |
| multiple-linear-regression-normal | Performs linear regression of the dependent variable, `dv,' on multiple independent variables, `i... |
| multiple-linear-regression-verbose | Let m be the number of independent variables, `ivs.' This function returns fourteen values: 1. t... |
| multiple-modes | MULTIPLE-MODES (DATA K &KEY START END KEY) Returns the `k' most frequent elements of `data,' whic... |
| multiple-modes-internal | See MULTIPLE-MODES |
| multiply-matrices | Multiply matrices MATRIX-1 and MATRIX-2, storing into MATRIX-3 if supplied. If MATRIX-3 is not su... |
| normalize-matrix | Returns a new matrix such that the sum of its elements is 1.0 |
| on-interval | returns t iff x in the interval |
| partials-from-parents | |
| permutation-count | Returns the number of possible ways of taking k elements out of n total. |
| poisson-cdf | Computes the cumulative distribution function for a Poisson random variable with mean `x' evaluat... |
| print-anova-table | Prints `anova-table' on `stream.' |
| print-scheffe-table | Prints `scheffe-table' on `stream.' If the original one-way anova data had N groups, the Scheffe ... |
| pythag-df | Computes square root of a*a + b*b without destructive overflow or underflow. |
| pythag-sf | Computes square root of a*a + b*b without destructive overflow or underflow. |
| quantile | QUANTILE (DATA Q &KEY START END KEY) Returns the element which is the q'th percentile of the data... |
| quantile-internal | See QUANTILE |
| r-score | Takes two sequences and returns the correlation coefficient. Formula: Sum (Cross-product (Differ... |
| radians->degrees | Convert radians to degrees. Does not round the result. |
| range | RANGE (DATA &KEY START END KEY) Returns the range of the sequence `data.' Signals `no-data' if th... |
| range-internal | See RANGE |
| reduce-matrix | Uses the Gauss-Jordan reduction method to reduce a matrix. |
| remove-&rest | Removes the '&rest arg' part from a lambda-list (strictly for documentation purposes. |
| round-to-factor | Equivalent to (* factor (round n factor)). For example, `round-to-factor' of 65 and 60 is 60. U... |
| safe-exp | Eliminates floating point underflow for the exponential function. Instead, it just returns 0.0d0 |
| scalar-matrix-multiply | Multiplies a matrix by a scalar value in the form M[i,j] = s*M[i,j]. |
| scheffe-tests | Performs all pairwise comparisons between group means, testing for significance using Scheffe's F... |
| significance | SIGNIFICANCE NIL NIL |
| significance-internal | |
| singular-value-decomposition | Returns as three values the U W and V of singular value decomposition. If you have already conse... |
| skewness | SKEWNESS (DATA &KEY START END KEY) Returns the skewness of `data', which is the sum of cubed dist... |
| skewness-internal | See SKEWNESS |
| smart-mode | |
| smooth-4253h | Smooths `data' by successive smoothing: 4,median; then 2,median; then 5,median; then 3,median; th... |
| smooth-hanning | Smooths `data' by replacing each element with the weighted mean of it and its two neighbors. The... |
| smooth-mean-2 | With a window of size two, the median and mean smooth functions are the same. |
| smooth-mean-3 | Smooths `data' by replacing each element with the mean of it and its two neighbors. The ends are... |
| smooth-mean-4 | Smooths `data' by replacing each element with the mean of it, its left neighbor, and its two righ... |
| smooth-mean-5 | Smooths `data' by replacing each element with the median of it, its two left neighbors and its tw... |
| smooth-median-2 | Smooths `data' by replacing each element with the median of it and its neighbor on the left. A m... |
| smooth-median-3 | Smooths `data' by replacing each element with the median of it and its two neighbors. The ends a... |
| smooth-median-4 | Smooths `data' by replacing each element with the median of it, its left neighbor, and its two ri... |
| smooth-median-5 | Smooths `data' by replacing each element with the median of it, its two left neighbors and its tw... |
| square | |
| standard-deviation | STANDARD-DEVIATION (DATA &KEY START END KEY) Returns the standard deviation of `data,' which is j... |
| standard-deviation-internal | See STANDARD-DEVIATION |
| statistical-summary | STATISTICAL-SUMMARY (DATA &KEY START END KEY) Compute the length, minimum, maximum, range, median... |
| statistical-summary-internal | See STATISTICAL-SUMMARY |
| students-t-significance | Student's distribution is much like the Gaussian distribution except with heavier tails, dependin... |
| sum-list | Takes a sequence of numbers and returns their sum. Formula: Sum(X). |
| sum-of-array-elements | |
| sum-of-squares | Returns the sum of squared distances from the mean of `data'. Signals `no-data' if there is no d... |
| svbksb-df | Solves A X = B for a vector `X,' where A is specified by the mxn array U, `n' vector W, and nxn m... |
| svbksb-sf | Solves A X = B for a vector `X,' where A is specified by the mxn array U, `n' vector W, and nxn m... |
| svd-back-substitute | Returns the solution vector to the Ax=b, where A has been decomposed into `u,' `w' and `v' by `si... |
| svd-inverse-fast-df | Computes the inverse of a matrix that has been decomposed into `u,' `w' and `v' by singular value... |
| svd-inverse-fast-sf | Computes the inverse of a matrix that has been decomposed into `u,' `w' and `v' by singular value... |
| svd-inverse-slow-df | Computes the inverse of a matrix that has been decomposed into `u,' `w' and `v' by singular value... |
| svd-inverse-slow-sf | Computes the inverse of a matrix that has been decomposed into `u,' `w' and `v' by singular value... |
| svd-matrix-inverse | Use singular value decomposition to compute the inverse of `A.' If an exact inverse is not possib... |
| svd-solve-linear-system | Returns solution of linear system matrix * solution = b-vector. Employs the singular value decom... |
| svd-zero | If the relative magnitude of an element in `w' compared to the largest element is less than `thre... |
| svdcmp-df | Given an `m'x`n' matrix `A,' this routine computes its singular value decomposition, A = U W V^T.... |
| svdcmp-sf | Given an `m'x`n' matrix `A,' this routine computes its singular value decomposition, A = U W V^T.... |
| svdvar | Given `v' and `w' as computed by singular value decomposition, computes the covariance matrix amo... |
| svzero-df | If the relative magnitude of an element in `w' compared to the largest element is less than `thre... |
| svzero-sf | If the relative magnitude of an element in `w' compared to the largest element is less than `thre... |
| t-significance | T-SIGNIFICANCE NIL NIL |
| t-significance-internal | |
| t-test | T-TEST (SAMPLE-1 SAMPLE-2 &OPTIONAL (TAILS BOTH) (H0MEAN 0)) Returns the t-statistic for the diff... |
| t-test-internal | See T-TEST |
| t-test-matched | T-TEST-MATCHED (SAMPLE1 SAMPLE2 &OPTIONAL (TAILS BOTH)) Returns the t-statistic for two matched s... |
| t-test-matched-internal | See T-TEST-MATCHED |
| t-test-one-sample | T-TEST-ONE-SAMPLE (DATA TAILS &OPTIONAL (H0-MEAN 0) &KEY START END KEY) Returns the t-statistic f... |
| t-test-one-sample-internal | See T-TEST-ONE-SAMPLE |
| times2 | Multiply `i' by a power of 2. |
| transpose-matrix | |
| trimmed-mean | TRIMMED-MEAN (DATA PERCENTAGE &KEY START END KEY) Returns a trimmed mean of `data.' A trimmed mea... |
| trimmed-mean-internal | See TRIMMED-MEAN |
| trunc2 | Truncate `n' to a power of 2. |
| truncate-to-factor | Equivalent to (* factor (truncate n factor)). For example, `truncate-to-factor' of 65 and 60 is ... |
| tukey-summary | TUKEY-SUMMARY (DATA &KEY START END KEY) Computes a Tukey five-number summary of the data. That i... |
| tukey-summary-internal | See TUKEY-SUMMARY |
| variance | VARIANCE (DATA &KEY START END KEY) Returns the variance of `data,' that is, the `sum-of-squares' ... |
| variance-internal | See VARIANCE |
| z-test-one-sample | Z-TEST-ONE-SAMPLE (DATA TAILS &OPTIONAL (H0-MEAN 0) (H0-STD-DEV 1) &KEY START ... |
| z-test-one-sample-internal | See Z-TEST-ONE-SAMPLE |
| composite-statistic-p | |
|---|---|
| convert | |
| cross-product | |
| dot-product | http://en.wikipedia.org/wiki/Dot_product |
| make-statistic | |
| simple-statistic-p | |
| statisticp |
| aref1 | |
|---|---|
| aref11 | |
| check-type-of-arg | Generate error if the value of ARG-NAME doesn't satisfy PREDICATE. PREDICATE is a function name (... |
| define-statistic | In clasp, statistical objects have two parts, a class which stores the various parts of the objec... |
| sign-df | |
| sign-sf | |
| start/end | |
| underflow-goes-to-zero | Protects against floating point underflow errors and sets the value to 0.0 instead. |
| with-routine-error-handling | |
| with-temp-table | Binds `temp' to a hash table. |
| with-temp-vector | Binds `temp' to a vector of length at least `min-size.' It's a vector of pointers and has a fill-... |