# crossrun v0.1.0

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## Joint Distribution of Number of Crossings and Longest Run

Joint distribution of number of crossings and the longest run in a series of independent Bernoulli trials. The computations uses an iterative procedure where computations are based on results from shorter series. The procedure conditions on the start value and partitions by further conditioning on the position of the first crossing (or none).

## Functions in crossrun

 Name Description joint15symm Joint probabilities, n=15, symmetric case simclbin Simulation of Independent Bernoulli Observations joint100symm Joint probabilities, n=100, symmetric case joint60symm Joint probabilities, n=60, symmetric case joint15.6 Joint probabilities, n=15, success probability 0.6 clshift Number of Crossings and Longest Run joint60.6 Joint probabilities, 60, success probability 0.6 crossrunbin Joint Distribution for Crossings and Runs crossrunshift wrapper for crossrunbin, succes probability=pnorm(shift). crossrunchange Joint Distribution for Crossings and Runs, Varying Success Probability. cumsummcol Column-Wise Cumulative Sums cumsumm Row-wise Cumulative Sums boxprobt Box Cumulative Sums exactbin Exact Joint Probabilities for Low n joint100.6 Joint probabilities, n=100, success probability 0.6 crossrunsymm Joint Probabilities for Crossings and Runs, Symmetric Case No Results!