Provides method used to check whether data have outlier in efficiency measurement 
  of big samples with data envelopment analysis (DEA). In this jackstrap method, the package 
  provides two criteria to define outliers: heaviside and k-s test. The technique was developed 
  by Sousa and Stosic (2005) "Technical Efficiency of the Brazilian Municipalities: Correcting 
  Nonparametric Frontier Measurements for Outliers." <doi:10.1007/s11123-005-4702-4>.

Test for association between the observed data and their estimated latent variables. The jackstraw package provides a resampling strategy and testing scheme to estimate statistical significance of association between the observed data and their latent variables. Depending on the data type and the analysis aim, the latent variables may be estimated by principal component analysis (PCA), factor analysis (FA), K-means clustering, and related unsupervised learning algorithms. The jackstraw methods learn over-fitting characteristics inherent in this circular analysis, where the observed data are used to estimate the latent variables and used again to test against that estimated latent variables. When latent variables are estimated by PCA, the jackstraw enables statistical testing for association between observed variables and latent variables, as estimated by low-dimensional principal components (PCs). This essentially leads to identifying variables that are significantly associated with PCs. Similarly, unsupervised clustering, such as K-means clustering, partition around medoids (PAM), and others, finds coherent groups in high-dimensional data. The jackstraw estimates statistical significance of cluster membership, by testing association between data and cluster centers. Clustering membership can be improved by using the resulting jackstraw p-values and posterior inclusion probabilities (PIPs), with an application to unsupervised evaluation of cell identities in single cell RNA-seq (scRNA-seq).

Evaluation of the Jacobi theta functions and related
    functions: Weierstrass elliptic function, Weierstrass sigma function,
    Weierstrass zeta function, Klein j-function, Dedekind eta function,
    lambda modular function, Jacobi elliptic functions, Neville theta
    functions, Eisenstein series, lemniscate elliptic functions, elliptic 
    alpha function, Rogers-Ramanujan continued fractions, and Dixon 
    elliptic functions. Complex values of the variable are supported.