INFORMATION FOR: C:\SFW\FH\SOUTH.FHX, ALL 29 SERIES Minimum Samples Scarred: 1 Include Other Injuries : No Analysis based on site composite information. ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Fire Interval Analyses, All Scarred, 1600 - 1850 Part 1: Summary Information Total Recorder Percent Fire Year Scars Trees Scarred Interval --------------------------------------- 1604 1 5 20 . 1616 2 6 33 12 1623 1 8 13 7 1624 1 8 13 1 1644 1 10 10 20 1648 3 11 27 4 1656 1 11 9 8 1664 6 14 43 8 1672 1 13 8 8 1685 9 16 56 13 1696 1 18 6 11 1705 2 19 11 9 1715 3 19 16 10 1723 1 19 5 8 1724 1 19 5 1 1725 2 19 11 1 1729 5 19 26 4 1748 7 19 37 19 1761 1 19 5 13 1763 2 19 11 2 1773 1 18 6 10 1778 3 18 17 5 1779 2 18 11 1 1786 4 17 24 7 1794 1 16 6 8 1803 2 16 13 9 1810 1 17 6 7 1826 3 17 18 16 1827 1 17 6 1 1831 1 17 6 4 1842 6 13 46 11 1843 1 13 8 1 ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 2: Frequency Distribution, Actual Data Interval | Number | | Relative Frequency | | | | | | ---1---2---3---4---5---6---7---8---9--10--11--12--13--14 1 6 19.35 ]]]]]]]]]]]]]]]]]]]]]]]] 2 1 3.23 ]]]] 3 0 0.00 4 3 9.68 ]]]]]]]]]]]] 5 1 3.23 ]]]] 6 0 0.00 7 3 9.68 ]]]]]]]]]]]] 8 5 16.13 ]]]]]]]]]]]]]]]]]]]] 9 2 6.45 ]]]]]]]] 10 2 6.45 ]]]]]]]] 11 2 6.45 ]]]]]]]] 12 1 3.23 ]]]] 13 2 6.45 ]]]]]]]] 14 0 0.00 15 0 0.00 16 1 3.23 ]]]] 17 0 0.00 18 0 0.00 19 1 3.23 ]]]] 20 1 3.23 ]]]] ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 3: Kolmogorov-Smirnov Test for Goodness-of-Fit Ho: Data can be modeled with an empirical distribution. Ha: Data can not be modeled with an empirical distribution. Reject Ho if d-statistic is significant. Number Obs K-S d-statistic Prob > d 31 0.256 0.0339 ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 4: Two-Parameter Weibull Distribution Parameters Cumulative Dist. Function: F(fi) = 1-exp(-((fi-a)/b)^c) where fi > 0 = fire interval data, a = location parameter = 0, b = scale parameter, c = shape parameter Scale parameter : 8.45 Shape parameter : 1.44 ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 5: Kolmogorov-Smirnov Test for Goodness-of-Fit Ho: Weibull distribution models fire interval data adequately. Ha: Weibull distribution does not fit fire interval data adequately. Reject Ho if d-statistic is significant. Number Obs K-S d-statistic Prob > d 31 0.148 0.5043 ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 6: Weibull Distribution Exceedance Probability Table << = significantly short interval, >> = significantly long interval -------------------------- Exceedance Associated Probability Fire Interval -------------------------- 0.999 0.07 << 0.990 0.34 << 0.975 0.66 << 0.950 1.07 << 0.900 1.77 << 0.875 2.08 << 0.800 2.98 0.750 3.55 0.700 4.13 0.667 4.51 0.500 6.55 <- Weibull Median Interval 0.333 9.02 0.300 9.61 0.250 10.60 0.200 11.76 0.125 14.06 >> 0.100 15.09 >> 0.050 18.12 >> 0.025 20.95 >> 0.010 24.44 >> 0.001 32.40 >> ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 7: Two-Parameter Weibull Distribution Probabilities p > fi : 1 - c.d.f. = 1 - F(fi) = exp(-(fi/b)^c) h(t) : hazard function = c * (fi^(c-1)/b^c p.d.f. : prob. dist. func. = h(t) * (1 - F(fi)) > : significantly long interval < : significantly short interval Year fi p > fi h(t) p.d.f. ------------------------------------ 1604 . . . . 1616 12 0.191 0.198 0.038 1623 7 0.466 0.157 0.073 1624 1 < 0.955 0.067 0.064 1644 20 > 0.032 0.248 0.008 1648 4 0.711 0.123 0.087 1656 8 0.397 0.166 0.066 1664 8 0.397 0.166 0.066 1672 8 0.397 0.166 0.066 1685 13 0.156 0.206 0.032 1696 11 0.232 0.191 0.044 1705 9 0.335 0.175 0.059 1715 10 0.280 0.183 0.051 1723 8 0.397 0.166 0.066 1724 1 < 0.955 0.067 0.064 1725 1 < 0.955 0.067 0.064 1729 4 0.711 0.123 0.087 1748 19 > 0.040 0.243 0.010 1761 13 0.156 0.206 0.032 1763 2 < 0.882 0.091 0.080 1773 10 0.280 0.183 0.051 1778 5 0.625 0.135 0.085 1779 1 < 0.955 0.067 0.064 1786 7 0.466 0.157 0.073 1794 8 0.397 0.166 0.066 1803 9 0.335 0.175 0.059 1810 7 0.466 0.157 0.073 1826 16 > 0.082 0.225 0.018 1827 1 < 0.955 0.067 0.064 1831 4 0.711 0.123 0.087 1842 11 0.232 0.191 0.044 1843 1 < 0.955 0.067 0.064 ------------------------------------ ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 8: Summary Statistics Total Intervals : 31 Mean Fire Interval : 7.71 Median Fire Interval : 8.00 Weibull Modal Interval : 3.70 Weibull Median Interval : 6.55 Fire Frequency : 0.15 Standard Deviation : 5.20 Coefficient of Variation : 0.67 Skewness : 0.51 Kurtosis : -0.27 Scale parameter : 8.45 Shape parameter : 1.44 Minimum Fire Interval : 1.00 Maximum Fire Interval : 20.00 Lower Exceedance Interval : 2.08 Upper Exceedance Interval : 14.06 Maximum Hazard Interval : 355.13 ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Fire Interval Analyses, >= 10% Scarred, 1600 - 1850 Part 1: Summary Information Total Recorder Percent Fire Year Scars Trees Scarred Interval --------------------------------------- 1604 1 5 20 . 1616 2 6 33 12 1623 1 8 13 7 1624 1 8 13 1 1644 1 10 10 20 1648 3 11 27 4 1664 6 14 43 16 1685 9 16 56 21 1705 2 19 11 20 1715 3 19 16 10 1725 2 19 11 10 1729 5 19 26 4 1748 7 19 37 19 1763 2 19 11 15 1778 3 18 17 15 1779 2 18 11 1 1786 4 17 24 7 1803 2 16 13 17 1826 3 17 18 23 1842 6 13 46 16 ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 2: Frequency Distribution, Actual Data Interval | Number | | Relative Frequency | | | | | | ---1---2---3---4---5---6---7---8---9--10--11--12--13--14 1 2 10.53 ]]]]]]]] 2 0 0.00 3 0 0.00 4 2 10.53 ]]]]]]]] 5 0 0.00 6 0 0.00 7 2 10.53 ]]]]]]]] 8 0 0.00 9 0 0.00 10 2 10.53 ]]]]]]]] 11 0 0.00 12 1 5.26 ]]]] 13 0 0.00 14 0 0.00 15 2 10.53 ]]]]]]]] 16 2 10.53 ]]]]]]]] 17 1 5.26 ]]]] 18 0 0.00 19 1 5.26 ]]]] 20 2 10.53 ]]]]]]]] 21 1 5.26 ]]]] 22 0 0.00 23 1 5.26 ]]]] ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 3: Kolmogorov-Smirnov Test for Goodness-of-Fit Ho: Data can be modeled with an empirical distribution. Ha: Data can not be modeled with an empirical distribution. Reject Ho if d-statistic is significant. Number Obs K-S d-statistic Prob > d 19 0.178 0.5803 ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 4: Two-Parameter Weibull Distribution Parameters Cumulative Dist. Function: F(fi) = 1-exp(-((fi-a)/b)^c) where fi > 0 = fire interval data, a = location parameter = 0, b = scale parameter, c = shape parameter Scale parameter : 13.89 Shape parameter : 1.74 ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 5: Kolmogorov-Smirnov Test for Goodness-of-Fit Ho: Weibull distribution models fire interval data adequately. Ha: Weibull distribution does not fit fire interval data adequately. Reject Ho if d-statistic is significant. Number Obs K-S d-statistic Prob > d 19 0.164 0.6887 ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 6: Weibull Distribution Exceedance Probability Table << = significantly short interval, >> = significantly long interval -------------------------- Exceedance Associated Probability Fire Interval -------------------------- 0.999 0.26 << 0.990 0.99 << 0.975 1.68 << 0.950 2.53 << 0.900 3.82 << 0.875 4.37 << 0.800 5.87 0.750 6.79 0.700 7.69 0.667 8.27 0.500 11.25 <- Weibull Median Interval 0.333 14.66 0.300 15.45 0.250 16.75 0.200 18.25 0.125 21.13 >> 0.100 22.41 >> 0.050 26.06 >> 0.025 29.36 >> 0.010 33.35 >> 0.001 42.08 >> ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 7: Two-Parameter Weibull Distribution Probabilities p > fi : 1 - c.d.f. = 1 - F(fi) = exp(-(fi/b)^c) h(t) : hazard function = c * (fi^(c-1)/b^c p.d.f. : prob. dist. func. = h(t) * (1 - F(fi)) > : significantly long interval < : significantly short interval Year fi p > fi h(t) p.d.f. ------------------------------------ 1604 . . . . 1616 12 0.461 0.113 0.052 1623 7 0.739 0.075 0.056 1624 1 < 0.990 0.018 0.018 1644 20 0.151 0.165 0.025 1648 4 < 0.892 0.050 0.044 1664 16 0.278 0.139 0.039 1685 21 0.128 0.171 0.022 1705 20 0.151 0.165 0.025 1715 10 0.569 0.098 0.056 1725 10 0.569 0.098 0.056 1729 4 < 0.892 0.050 0.044 1748 19 0.178 0.158 0.028 1763 15 0.319 0.133 0.042 1778 15 0.319 0.133 0.042 1779 1 < 0.990 0.018 0.018 1786 7 0.739 0.075 0.056 1803 17 0.241 0.146 0.035 1826 23 > 0.090 0.183 0.016 1842 16 0.278 0.139 0.039 ------------------------------------ ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 8: Summary Statistics Total Intervals : 19 Mean Fire Interval : 12.53 Median Fire Interval : 15.00 Weibull Modal Interval : 8.51 Weibull Median Interval : 11.25 Fire Frequency : 0.09 Standard Deviation : 6.98 Coefficient of Variation : 0.56 Skewness : -0.26 Kurtosis : -1.27 Scale parameter : 13.89 Shape parameter : 1.74 Minimum Fire Interval : 1.00 Maximum Fire Interval : 23.00 Lower Exceedance Interval : 4.37 Upper Exceedance Interval : 21.13 Maximum Hazard Interval : 189.48 ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Fire Interval Analyses, >= 25% Scarred, 1600 - 1850 Part 1: Summary Information Total Recorder Percent Fire Year Scars Trees Scarred Interval --------------------------------------- 1616 2 6 33 . 1648 3 11 27 32 1664 6 14 43 16 1685 9 16 56 21 1729 5 19 26 44 1748 7 19 37 19 1842 6 13 46 94 ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 2: Frequency Distribution, Actual Data Interval | Number | | Relative Frequency | | | | | | ---1---2---3---4---5---6---7---8---9--10--11--12--13--14 1 0 0.00 2 0 0.00 3 0 0.00 4 0 0.00 5 0 0.00 6 0 0.00 7 0 0.00 8 0 0.00 9 0 0.00 10 0 0.00 11 0 0.00 12 0 0.00 13 0 0.00 14 0 0.00 15 0 0.00 16 1 16.67 ]]]] 17 0 0.00 18 0 0.00 19 1 16.67 ]]]] 20 0 0.00 21 1 16.67 ]]]] 22 0 0.00 23 0 0.00 24 0 0.00 25 0 0.00 26 0 0.00 27 0 0.00 28 0 0.00 29 0 0.00 30 0 0.00 >30 3 50.00 ]]]]]]]]]]]] ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 3: Kolmogorov-Smirnov Test for Goodness-of-Fit Ho: Data can be modeled with an empirical distribution. Ha: Data can not be modeled with an empirical distribution. Reject Ho if d-statistic is significant. Number Obs K-S d-statistic Prob > d 6 0.365 0.4001 ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 4: Two-Parameter Weibull Distribution Parameters Cumulative Dist. Function: F(fi) = 1-exp(-((fi-a)/b)^c) where fi > 0 = fire interval data, a = location parameter = 0, b = scale parameter, c = shape parameter Scale parameter : 42.39 Shape parameter : 1.56 ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 5: Kolmogorov-Smirnov Test for Goodness-of-Fit Ho: Weibull distribution models fire interval data adequately. Ha: Weibull distribution does not fit fire interval data adequately. Reject Ho if d-statistic is significant. Number Obs K-S d-statistic Prob > d 6 0.215 0.9439 ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 6: Weibull Distribution Exceedance Probability Table << = significantly short interval, >> = significantly long interval -------------------------- Exceedance Associated Probability Fire Interval -------------------------- 0.999 0.50 << 0.990 2.20 << 0.975 3.99 << 0.950 6.28 << 0.900 9.98 << 0.875 11.62 << 0.800 16.17 0.750 19.03 0.700 21.85 0.667 23.73 0.500 33.49 <- Weibull Median Interval 0.333 45.03 0.300 47.76 0.250 52.29 0.200 57.56 0.125 67.86 >> 0.100 72.45 >> 0.050 85.80 >> 0.025 98.08 >> 0.010 113.12 >> 0.001 146.79 >> ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 7: Two-Parameter Weibull Distribution Probabilities p > fi : 1 - c.d.f. = 1 - F(fi) = exp(-(fi/b)^c) h(t) : hazard function = c * (fi^(c-1)/b^c p.d.f. : prob. dist. func. = h(t) * (1 - F(fi)) > : significantly long interval < : significantly short interval Year fi p > fi h(t) p.d.f. ------------------------------------ 1616 . . . . 1648 32 0.524 0.031 0.016 1664 16 0.803 0.021 0.017 1685 21 0.715 0.025 0.018 1729 44 0.347 0.037 0.013 1748 19 0.751 0.023 0.018 1842 94 > 0.032 0.057 0.002 ------------------------------------ ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== Part 8: Summary Statistics Total Intervals : 6 Mean Fire Interval : 37.67 Median Fire Interval : 26.50 Weibull Modal Interval : 21.88 Weibull Median Interval : 33.49 Fire Frequency : 0.03 Standard Deviation : 29.47 Coefficient of Variation : 0.78 Skewness : 1.23 Kurtosis : -0.22 Scale parameter : 42.39 Shape parameter : 1.56 Minimum Fire Interval : 16.00 Maximum Fire Interval : 94.00 Lower Exceedance Interval : 11.62 Upper Exceedance Interval : 67.86 Maximum Hazard Interval : > 1000 ===================================================================== [*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*][*] ===================================================================== -=< End of Fire Interval Analysis >=-