Here is an example. The Flamingo Hotel is located on the beach in the southern Sardinia, about 40 kilometers from Cagliari. Of interest is the length of stay (LOS). The spikeplot on the right shows spikes at 7 and 14 days. Two reasons for this are obvious: people book in units of weeks for convenience and take advantage of weekly specials such as staying 7 nights for the cost of 6. A long-tailed distribution such as the logarithmic or zeta could be used to model the parent and the spikes by parametric inflation. Probably one of values 1 and 2 need to be adjusted for the other.
Here is an example. The figure on the left is a plot of the self-reported ages at which smokers quit their habit. The data come from a large cross-sectional health study from the mid-1990s in New Zealand. Many quitters report an age that is a multiple of 5, such as 30, 35, 40, 45, 50. Values such as 29 and 31 are seeped. Many of the spikes can be treated as coming from a (second) negative binomial distribution, which is a suitable parent. It transpires that a GI-NBD can give a reasonable fit. In general, heaping is a common problem in surveys where self-reported data is collected. There are many examples from the literature, e.g., income, age, household expenditure, working hours. Most respondents know approximately the true value so that the response is contaminated by measurement error. GAITD regression holds promise for heaped and seeped data.