Just some extra comments and tests

I tested the weighted std and avg again, with a scenario where the random generator is starting at max=30 increments over time up to max=300 and decrement back to 30 to see how long it takes to adjust.
2 periods of 2097152 samples seems to be enough to get close.

I think this weight is making sense for a server running over a long period of time.
But we could adjust the period based on ping interval to make sure it is matching clear time period.

The stdev in the middle of the scenario at max 300 is accurate 86.74 in libre office

total[56623104]max[300] M2[15362844409.015831] count[2097152] std[85.589592] avg[148.497940] est[186.914322]

total[2097152]max[30] M2[157100024.339350] count[2097152] std[8.655124] avg[15.495893] est[13.079656]
total[4194304]max[60] M2[565161279.098511] count[2097152] std[16.416151] avg[24.987877] est[27.263668]
total[6291456]max[60] M2[619712983.957470] count[2097152] std[17.190182] avg[28.423359] est[29.659512]
total[8388608]max[60] M2[627188475.025724] count[2097152] std[17.293550] avg[29.725079] est[32.875008]
total[10485760]max[90] M2[1247094770.763514] count[2097152] std[24.385681] avg[39.690018] est[45.258430]
total[12582912]max[90] M2[1369149290.866558] count[2097152] std[25.551155] avg[43.338192] est[55.149673]
total[14680064]max[90] M2[1399719270.525143] count[2097152] std[25.834831] avg[44.726627] est[47.590252]
total[16777216]max[120] M2[2226973264.366464] count[2097152] std[32.586872] avg[54.664543] est[61.240814]
total[18874368]max[120] M2[2426866858.845158] count[2097152] std[34.017948] avg[58.319107] est[67.435730]
total[20971520]max[120] M2[2485716268.964881] count[2097152] std[34.427933] avg[59.637623] est[48.287968]
total[23068672]max[150] M2[3523236730.424239] count[2097152] std[40.987938] avg[69.647438] est[80.191017]
total[25165824]max[150] M2[3795763992.445277] count[2097152] std[42.543652] avg[73.368950] est[72.679794]
total[27262976]max[150] M2[3886770781.855125] count[2097152] std[43.050640] avg[74.759964] est[70.232475]
total[29360128]max[180] M2[5131618327.571171] count[2097152] std[49.466629] avg[84.692070] est[96.479042]
total[31457280]max[180] M2[5484142140.309916] count[2097152] std[51.137501] avg[88.429367] est[87.843102]
total[33554432]max[180] M2[5597876661.386850] count[2097152] std[51.665047] avg[89.803963] est[109.757233]
total[35651584]max[210] M2[7053724001.055486] count[2097152] std[57.995510] avg[99.741013] est[91.987564]
total[37748736]max[210] M2[7479776962.029222] count[2097152] std[59.721329] avg[103.352173] est[97.751457]
total[39845888]max[210] M2[7630976936.031951] count[2097152] std[60.321930] avg[104.694923] est[115.147377]
total[41943040]max[240] M2[9292088622.916683] count[2097152] std[66.564369] avg[114.621590] est[150.303802]
total[44040192]max[240] M2[9796104291.010365] count[2097152] std[68.345802] avg[118.272659] est[122.886292]
total[46137344]max[240] M2[9965937966.086864] count[2097152] std[68.935707] avg[119.582924] est[93.705055]
total[48234496]max[270] M2[11848203838.922304] count[2097152] std[75.164261] avg[129.532562] est[144.145126]
total[50331648]max[270] M2[12425804190.196043] count[2097152] std[76.974594] avg[133.170563] est[127.568375]
total[52428800]max[270] M2[12618113837.423813] count[2097152] std[77.567963] avg[134.508347] est[132.567368]
total[54525952]max[300] M2[14713927465.674479] count[2097152] std[83.762466] avg[144.738953] est[157.351410]
total[56623104]max[300] M2[15362844409.015831] count[2097152] std[85.589592] avg[148.497940] est[186.914322]
total[58720256]max[300] M2[15597086896.549715] count[2097152] std[86.239632] avg[149.828369] est[134.888901]
total[60817408]max[270] M2[13897060743.879736] count[2097152] std[81.404167] avg[140.986145] est[148.230011]
total[62914560]max[270] M2[13179605332.005194] count[2097152] std[79.275017] avg[137.667099] est[147.819626]
total[65011712]max[270] M2[12904876783.172298] count[2097152] std[78.444427] avg[136.416397] est[174.410904]
total[67108864]max[240] M2[11234667410.652538] count[2097152] std[73.192276] avg[126.221443] est[116.936584]
total[69206016]max[240] M2[10506238432.030697] count[2097152] std[70.779709] avg[122.688011] est[147.278595]
total[71303168]max[240] M2[10232558486.513565] count[2097152] std[69.851746] avg[121.319862] est[135.017303]
total[73400320]max[210] M2[8753355360.939997] count[2097152] std[64.605934] avg[111.340347] est[102.771973]
total[75497472]max[210] M2[8109358941.663550] count[2097152] std[62.183964] avg[107.595718] est[103.639900]
total[77594624]max[210] M2[7858572277.892706] count[2097152] std[61.214874] avg[106.287216] est[121.709717]
total[79691776]max[180] M2[6591117074.132572] count[2097152] std[56.061493] avg[96.341568] est[85.318893]
total[81788928]max[180] M2[6022946657.180739] count[2097152] std[53.590729] avg[92.621536] est[70.211670]
total[83886080]max[180] M2[5803221389.644814] count[2097152] std[52.604115] avg[91.284225] est[91.405876]
total[85983232]max[150] M2[4742030532.232808] count[2097152] std[47.551838] avg[81.352226] est[65.601341]
total[88080384]max[150] M2[4247261369.886361] count[2097152] std[45.002811] avg[77.583412] est[58.726521]
total[90177536]max[150] M2[4050211394.232083] count[2097152] std[43.946468] avg[76.272026] est[94.734283]
total[92274688]max[120] M2[3200787916.367090] count[2097152] std[39.067318] avg[66.359764] est[59.015381]
total[94371840]max[120] M2[2785142322.233555] count[2097152] std[36.442558] avg[62.637939] est[62.011288]
total[96468992]max[120] M2[2617178115.333484] count[2097152] std[35.326595] avg[61.309391] est[61.678368]
total[98566144]max[90] M2[1981088219.305755] count[2097152] std[30.735271] avg[51.331150] est[43.893597]
total[100663296]max[90] M2[1640345108.679696] count[2097152] std[27.967443] avg[47.665287] est[45.548306]
total[102760448]max[90] M2[1500853910.913404] count[2097152] std[26.751883] avg[46.296799] est[48.260040]
total[104857600]max[60] M2[1071488249.817324] count[2097152] std[22.603664] avg[36.338905] est[29.824390]
total[106954752]max[60] M2[808602879.222455] count[2097152] std[19.635990] avg[32.646908] est[26.610825]
total[109051904]max[60] M2[697691376.099365] count[2097152] std[18.239664] avg[31.298117] est[30.748377]
total[111149056]max[30] M2[477998494.526686] count[2097152] std[15.097270] avg[21.326080] est[11.904392]
total[113246208]max[30] M2[291761992.912811] count[2097152] std[11.795042] avg[17.685249] est[15.319354]
total[115343360]max[30] M2[209023091.572831] count[2097152] std[9.983487] avg[16.296667] est[13.406508]

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