Estimating transition intensities in pure birth processes sampled in time
نویسنده
چکیده
We consider a situation where the state of a large number of independent pure birth processes, with common birth intensities, are observed at two time points. Estimates are derived, both when no restriction is placed on the intensities, and when they are assumed to follow a certain parametric model which assumes that the birth intensities are increasing. This is an assumptions that is sometimes made in the study of dynamic networks, where the births are interpreted as the occurrence of new edges. In this paper the theoretical results are applied to data from a survey of how the number of sexual contacts develops in time. The situation is generalized so that the birth intensities also depend on individual random factors. Di erent goodness-oft test of the models are considered.
منابع مشابه
Association Behaviour in Non-Linear Death Processes
Transition probabilities within a birth and death process are difficult to find analytically. As a consequence pure birth and pure death processes are considered in seperate systems and it is found that both systems can be fully specified from intensity specifications. In a linear continuous-time Markovian pure death process it is found that optional death times are independent. Faddy (1985) co...
متن کاملBirth and Death Processes with Absorption Mourad
Spectral measures and transition probabilities of birth and death processes with A0 #o 0 are obtained as limite when Ao 0+ of the corresponding quantities. In pa,rticula th(, case of finite population is discussed in full detail. Pure birth and death processes are used to derive an inequality for Dirichlet polynomials.
متن کاملMultivariate Risk Processes with Interacting Intensities
The classical models in risk theory consider a single type of claims. In the insurance business, however, several business lines with separate claim arrival processes appear naturally, and the individual claim processes may not be independent. We introduce a new class of models for such situations, where the underlying counting process is a multivariate continuous time Markov chain of pure birt...
متن کاملThe Effect of Different Light Intensities on Physiological and Biochemical Responses in Cyanobacterium Schizothrix vaginata under Naphtalene Treatment
Petroleum hydrocarbons pollution is one of the problems in the environment due to petroleum industry processes. Biological methods are novel routs to defend against them. In this research, the effect of light intensities on biodegradation of naphthalene and the physiological responses of cyanobacterium Schizothrix vaginata is investigated. In this order, studied cyanobacterium transfered to liq...
متن کاملModified Maximum Likelihood Estimation in First-Order Autoregressive Moving Average Models with some Non-Normal Residuals
When modeling time series data using autoregressive-moving average processes, it is a common practice to presume that the residuals are normally distributed. However, sometimes we encounter non-normal residuals and asymmetry of data marginal distribution. Despite widespread use of pure autoregressive processes for modeling non-normal time series, the autoregressive-moving average models have le...
متن کامل