I am a novice in statistics so please correct me if I am doing something fundamentally wrong. After wrestling for a long time with R in trying to fit my data to a good distribution, I figured out that it fits the Cauchy distribution with the following parameters:
location scale 37.029894 18.678936 ( 3.405665) ( 2.779136)
The data was from a survey where 100 people were asked how many friends they talked to over a period of 20 days and I am trying to see if it fits a known distribution. I generated the QQ-plot with the reference line and it looks like the image given below. From what I have been reading on the web, if the points fall close to the reference line then it is a good evidence that the data comes from this distribution.
So, is this a good evidence to say that the distribution is Cauchy or do I need to run any more tests? If so, can someone tell me the physical interpretation of this result? I mean, I read that if the data falls into a Cauchy distribution, then it will not have a mean and standard deviation but can someone help me understand this in plain English? If it does not have a mean then from what I understand, I cannot sample from this distribution. What is one supposed to infer about the population based on this result? Or should I be looking at other models?
UPDATE: What am I trying to achieve? I am trying to evaluate how much time it takes for some arbitrary piece of information to propagate for a population of size X. As this depends on the communication patterns of people, what I was trying to do was to build a model that could use the information from the 100 people I surveyed to give me patterns for the X number where X could be 500 or 1000.
Density Distribution of my data
QQ-Plot when trying to fit a Normal distribution to my data
From all the suggestions, I think I now understand why this cannot be a Cauchy distribution. Thanks to everyone. @HairyBeast suggested that I look at a negative binomial distribution so I plotted the following as well:
QQ-Plot when Negative Binomial Distribution was used
Negative Binomial Distribution