I am trying to obtain the distribution of RSSI measurements collected from 802.15.4 devices like Zolertia Re-Motes. These devices provide RSSI values in dBm units with +/-1 dBm error in measurements. I have collected RSSI data in indoor environments and try to fit a distribution to RSSI data assuming Ricean fading.
Cumulative distribution function plots and Quantile-Quantile plots look promising for estimated distributions, but hypothesis tests like Kolmogorov-Smirnov two-sample test, $\chi^2$ tests are failing even with very low significance level.
I would like to know if it is okay to apply Hypothesis tests for checking distributions fitness to the data. The estimation procedure is as follows:
1. Collect RSSI samples.
2. Estimate parameters of a distribution using the Method of moments and MLE. 3. Generate random numbers from estimated distribution.
Details of hypothesis testing:
1. $\chi^2$ goodness of fit test: 36000 RSSI observations are used to compare the frequency distribution w.r.t. estimated pdf.
2. Two-sample Kolmogorov-Smirnov test: 36000 random numbers from estimated pdf are generated and they are compared against 36000 observed RSSI values to check if both samples are following the same distribution. ktest2() function provided by matlab is used for this test.