Collecting data through the Internet surveys is useful either for marketing and other private research societies either statistical agencies and it has several advantages, such as low costs of collecting information, the speed of the data transmission and a possibility to monitor it. The usage of the electronic questionnaire in the Internet survey makes the interview more efficient, lowers the workload of the respondents and controls the responds’ quality. But the basic problem in the surveys over the Internet is concerned with collecting data sets according to classical methods of the sampling theory. In the Internet surveys drawing the sample is not possible and respondents are not randomly selected to the sample, but they participate in the survey with a subjective decision. The methods of the sampling theory can not be used for the data from such the samples because the probability inclusions are not known. In this paper we present basic characteristics of the Internet sample defined as the stochastic process and an example of an estimate of the rate of exponential distribution for three designs. In the first the time of the survey conducted is specified in advance and the size of the Internet sample is random value, in the second the size of the Internet sample is specified in advance and the time of the survey conducting is random value, in the third, both, the time of the survey conducting and the size of the Internet sample are specified in advance. Model based approach is proposed to estimate of parameters of the population.