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Inference for the truncated exponential distribution

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Abstract

The constructed estimator is introduced for the right truncation point of the truncated exponential distribution. The new estimator is most efficient in important ranges of truncation points for finite sample sizes. The introduced inverse mean squared error clearly indicates the good behaviour of the new estimator. The estimation of the scaling parameter is considered in all discussions and computations. The methods and models of the extreme value theory are not appropriate to estimate the truncation point because they work only in the case of very large sample sizes. Furthermore, a procedure for a first goodness-of-fit test is introduced. All this has been researched by extensive Monte Carlo simulations for different truncation points and sample sizes. Finally, the new inference methods are applied at the end for the random distribution of wildfire sizes and earthquake magnitudes.

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Acknowledgement

The author thanks S.G. Cumming for providing wildfire data.

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Authors and Affiliations

  1. Gustav-Freytag-Str. 24, Leipzig, Germany

    Mathias Raschke

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  1. Mathias Raschke
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Correspondence to Mathias Raschke.

Appendix

Appendix

See Tables 2, 3, 4, 5, 6 7, 8 and 9.

Table 2 Bias and MSE of \( \hat{\theta}\) for sample size n = 20
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Table 3 Bias and MSE of \( \hat{T} \) for sample size n = 20
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Table 4 Bias and MSE of \( \hat{\theta}\) for sample size n = 100
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Table 5 Bias and MSE of \( \hat{T} \) for sample size n = 100
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Table 6 Inverse Bias and inverse MSE of T for sample size n = 20
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Table 7 Inverse Bias and inverse MSE of T for sample size n = 100
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Table 8 Ratio of rejections with the Anderson–Darling test for the exponential distribution for sample size n = 20 and different levels of significance α
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Table 9 Ratio of rejections with the Anderson–Darling test for the exponential distribution for sample size n = 100 and different levels of significance α
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Raschke, M. Inference for the truncated exponential distribution. Stoch Environ Res Risk Assess 26, 127–138 (2012). https://doi.org/10.1007/s00477-011-0458-8

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