I would greatly appreciate in advance if you could help solve our stats problem during the design of a cableless LoRa gateway for communication. We have our gateways fed by solar energy and the intention is to find out the probability of time our gateway would be operational by continuous generation of solar energy in the presence of sunlight (Good Days) and the probability of time our gateway would go off (non operational) because of no solar energy generation (rainy and cloudy days), we call them bad days. Being simple enough: What is the probability that we have exactly 5 days of bad whether over a period of 1 month (30 days)? Extending this concept, What is the probability that we have 10 bad days of whether over a period of 1 month. and how can we combine them both? Thanks in anticipation
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$\begingroup$ These questions concern matters of fact, and so their answers are determined by looking at the meteorological record. They cannot be answered purely by calculations. $\endgroup$– whuber ♦Feb 7, 2018 at 14:53
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$\begingroup$ Thanks for your reply.being this a part of research article, we dont want it to be region specific instead it should be of generic type. We already included the aspect to make it operational for 7 consecutive days of bad whether as the accumulated energy would be enough for this period. But, there was a comment on it to improve it keeping in view the fact, there may be longer bad periods. what we are planning is, if we could give the probability of down times assuming 4 scenarios, 5,10,15,20 days of bad whether in a month. Any Suggestion to model it. $\endgroup$– Husnain SheraziFeb 7, 2018 at 16:16
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$\begingroup$ Since days of insolation are strongly region specific (as well as seasonal), it's hard to see how you can get away from that. Certainly you can study how your system fares under different scenarios. But it seems probability wouldn't play any meaningful role there, nor would it be possible to construct a physically defensible model without at least looking at actual meteorological records! $\endgroup$– whuber ♦Feb 7, 2018 at 17:54
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I could try to build out-of-hat some way to model those probabilities, working under different assumptions. However I strongly suggest to use prior knowledge and collect as many data as possible about weather in your specific location, labeling it as you wish and study the properties of that data. For a specific location it is much better than building an estimate using only uninformative priors like the probability to have a bad day is equal with having a good one.
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$\begingroup$ Thanks for your reply.being this a part of research article, we dont want it to be region specific instead it should be of generic type. We already included the aspect to make it operational for 7 consecutive days of bad whether as the accumulated energy would be enough for this period. But, there was a comment on it to improve it keeping in view the fact, there may be longer bad periods. what we are planning is, if we could give the probability of down times assuming 4 scenarios, 5,10,15,20 days of bad whether in a month. Any Suggestion to model it. $\endgroup$ Feb 7, 2018 at 16:13