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Analysis of rounded exponential data

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  • Gunnar Taraldsen

Abstract

The problem of inference based on a rounded random sample from the exponential distribution is treated. The main results are given by an explicit expression for the maximum-likelihood estimator, a confidence interval with a guaranteed level of confidence, and a conjugate class of distributions for Bayesian analysis. These results are exemplified on two concrete examples. The large and increasing body of results on the topic of grouped data has been mostly focused on the effect on the estimators. The methods and results for the derivation of confidence intervals here are hence of some general theoretical value as a model approach for other parametric models. The Bayesian credibility interval recommended in cases with a lack of other prior information follows by letting the prior equal the inverted exponential with a scale equal to one divided by the resolution. It is shown that this corresponds to the standard non-informative prior for the scale in the case of non-rounded data. For cases with the absence of explicit prior information it is argued that the inverted exponential prior with a scale given by the resolution is a reasonable choice for more general digitized scale families also.

Suggested Citation

  • Gunnar Taraldsen, 2011. "Analysis of rounded exponential data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 977-986, February.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:5:p:977-986
    DOI: 10.1080/02664761003692431
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    References listed on IDEAS

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    1. Lidong, E. & Hannig, Jan & Iyer, Hari, 2008. "Fiducial Intervals for Variance Components in an Unbalanced Two-Component Normal Mixed Linear Model," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 854-865, June.
    2. Anders Hald, 2001. "On the History of the Correction for Grouping, 1873–1922," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 417-428, September.
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    Cited by:

    1. K.O. Ekvall & M. Bottai, 2023. "Concave likelihood‐based regression with finite‐support response variables," Biometrics, The International Biometric Society, vol. 79(3), pages 2286-2297, September.
    2. Francisco Blasques & Vladim'ir Hol'y & Petra Tomanov'a, 2018. "Zero-Inflated Autoregressive Conditional Duration Model for Discrete Trade Durations with Excessive Zeros," Papers 1812.07318, arXiv.org, revised Jan 2022.

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