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Existence and uniqueness of the MLEs for normal distribution based on general progressively type-II censored samples. (English) Zbl 1116.62320
Summary: We prove that the MLEs of the parameters \(\mu\) and \(\sigma\) of a normal population, based on general progressively Type-II censored samples, exist and are unique.

MSC:
62F10 Point estimation
62N01 Censored data models
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References:
[1] Balakrishnan, N.; Aggarwala, R., Progressive censoring: theory, methods, and applications, (2000), Birkhaüser Boston
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[3] Balakrishnan, N.; Kannan, N.; Lin, C.-T.; Ng, H.K.T., Point & interval estimation for the normal distribution based on progressively type-II censored samples, IEEE trans. reliab., 52, 90-95, (2003)
[4] Mäkeläinen, T.; Schmidt, K.; Styan, G.P.H., On the existence and uniqueness of the maximum likelihood estimate of a vector-valued parameter in fixed-size samples, Ann. statist., 9, 758-767, (1981) · Zbl 0473.62004
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