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Table 5 Approximation for the tail probability of local trend score (LT score) versus the simulated probability \(P(LT(D)/\sqrt {1.25 n} \geq x)\). The approximate probability based on equation (7) is given in the 2nd column and the probability that \(LT(D)/\sqrt {1.25 n} \geq x\) from simulations is given in the 3rd to the 9th columns. Here, D=3

From: Statistical significance approximation in local trend analysis of high-throughput time-series data using the theory of Markov chains

   The number of time points n
x Approximation 10 20 30 40 60 80 100
2.0 0.7539 0.1130 0.4402 0.3841 0.4214 0.4882 0.5808 0.5319
2.2 0.5616 0.1130 0.2688 0.2530 0.3015 0.2901 0.3974 0.3751
2.4 0.3779 0.0278 0.1451 0.1643 0.2079 0.2164 0.2475 0.2473
2.6 0.2336 0.0047 0.0762 0.0992 0.0869 0.1131 0.1471 0.1165
2.8 0.1346 0.0047 0.0324 0.0308 0.0535 0.0538 0.0804 0.0682
3.0 0.0732 0.0000 0.0130 0.0169 0.0171 0.0344 0.0423 0.0393
3.2 0.0379 0.0000 0.0048 0.0072 0.0084 0.0140 0.0198 0.0206
3.4 0.0187 0.0000 0.0005 0.0041 0.0024 0.0046 0.0061 0.0060
3.6 0.0089 0.0000 0.0005 0.0008 0.0010 0.0016 0.0037 0.0026
3.8 0.0040 0.0000 0.0000 0.0003 0.0005 0.0008 0.0015 0.0015
4.0 0.0018 0.0000 0.0000 0.0002 0.0001 0.0002 0.0003 0.0009
4.2 0.0007 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0002
4.4 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4.6 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000