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Computing and graphing probability values of pearson distributions: a SAS/IML macro.

ABSTRACT: Background:Any empirical data can be approximated to one of Pearson distributions using the first four moments of the data (Elderton WP, Johnson NL. Systems of Frequency Curves. 1969; Pearson K. Philos Trans R Soc Lond Ser A. 186:343-414 1895; Solomon H, Stephens MA. J Am Stat Assoc. 73(361):153-60 1978). Thus, Pearson distributions made statistical analysis possible for data with unknown distributions. There are both extant, old-fashioned in-print tables (Pearson ES, Hartley HO. Biometrika Tables for Statisticians, vol. II. 1972) and contemporary computer programs (Amos DE, Daniel SL. Tables of percentage points of standardized pearson distributions. 1971; Bouver H, Bargmann RE. Tables of the standardized percentage points of the pearson system of curves in terms of β 1 and β 2. 1974; Bowman KO, Shenton LR. Biometrika. 66(1):147-51 1979; Davis CS, Stephens MA. Appl Stat. 32(3):322-7 1983; Pan W. J Stat Softw. 31(Code Snippet 2):1-6 2009) available for obtaining percentage points of Pearson distributions corresponding to certain pre-specified percentages (or probability values; e.g., 1.0%, 2.5%, 5.0%, etc.), but they are little useful in statistical analysis because we have to rely on unwieldy second difference interpolation to calculate a probability value of a Pearson distribution corresponding to a given percentage point, such as an observed test statistic in hypothesis testing. Results:The present study develops a SAS/IML macro program to identify the appropriate type of Pearson distribution based on either input of dataset or the values of four moments and then compute and graph probability values of Pearson distributions for any given percentage points. Conclusions:The SAS macro program returns accurate approximations to Pearson distributions and can efficiently facilitate researchers to conduct statistical analysis on data with unknown distributions.

SUBMITTER: Yang Q

PROVIDER: S-EPMC6923921 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:We describe four novel algorithms, RNAhairpin, RNAmloopNum, RNAmloopOrder, and RNAmloopHP, which compute the Boltzmann partition function for global structural constraints-respectively for the number of hairpins, the number of multiloops, maximum order (or depth) of multiloops, and the simultaneous number of hairpins and multiloops. Given an RNA sequence of length n and a user-specified integer 0???K???n, RNAhairpin (resp. RNAmloopNum and RNAmloopOrder) computes the partition functions Z(k) for each 0???k???K in time O(K(2)n(3)) and space O(Kn(2)), while RNAmloopHP computes the partition functions Z(m, h) for 0???mm???M multiloops and 0???h???H hairpins, with run time O(M(2)H(2)n(3)) and space O(MHn(2)). In addition, programs such as RNAhairpin (resp. RNAmloopHP) sample from the low-energy ensemble of structures having h hairpins (resp. m multiloops and h hairpins), for given h, m. Moreover, by using the fast Fourier transform (FFT), RNAhairpin and RNAmloopNum have been improved to run in time O(n(4)) and space O(n(2)), although this improvement is not possible for RNAmloopOrder. We present two applications of the novel algorithms. First, we show that for many Rfam families of RNA, structures sampled from RNAmloopHP are more accurate than the minimum free-energy structure; for instance, sensitivity improves by almost 24% for transfer RNA, while for certain ribozyme families, there is an improvement of around 5%. Second, we show that the probabilities p(k)=Z(k)/Z of forming k hairpins (resp. multiloops) provide discriminating novel features for a support vector machine or relevance vector machine binary classifier for Rfam families of RNA. Our data suggests that multiloop order does not provide any significant discriminatory power over that of hairpin and multiloop number, and since these probabilities can be efficiently computed using the FFT, hairpin and multiloop formation probabilities could be added to other features in existent noncoding RNA gene finders. Our programs, written in C/C++, are publicly available online at: http://bioinformatics.bc.edu/clotelab/RNAparametric .

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Computing and graphing probability values of pearson distributions: a SAS/IML macro.

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