• Communications for Statistical Applications and Methods
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• v.30 no.2
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• pp.191-213
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• 2023

Unit distributions are frequently used in probability theory and statistics to depict meaningful variables having values between zero and one. Using convenient transformation, the unit inverse exponentiated weibull (UIEW) distribution, which is equally useful for modelling data on the unit interval, is proposed in this study. Quantile function, moments, incomplete moments, uncertainty measures, stochastic ordering, and stress-strength reliability are among the statistical properties provided for this distribution. To estimate the parameters associated to the recommended distribution, well-known estimation techniques including maximum likelihood, maximum product of spacings, least squares, weighted least squares, Cramer von Mises, Anderson-Darling, and Bayesian are utilised. Using simulated data, we compare how well the various estimators perform. According to the simulated outputs, the maximum product of spacing estimates has lower values of accuracy measures than alternative estimates in majority of situations. For two real datasets, the proposed model outperforms the beta, Kumaraswamy, unit Gompartz, unit Lomax and complementary unit weibull distributions based on various comparative indicators.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.2
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• pp.33.3-34
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• 2015

We present the spectroscopic study of the globular clusters (GCs) in the massive elliptical galaxy M86 in the Virgo galaxy cluster. Using the spectra obtained from the Multi-Object Spectroscopy (MOS) mode of Faint Object Camera and Spectrograph (FOCAS) on the Subaru Telescope, we measure the radial velocities for 56 GCs in M86. The mean velocity of the GCs is derived to be $<v_p>=-335{\pm}41km/s$, which is different from the velocity of the M86 nucleus ($<v_{gal}>=-224{\pm}5km/s$) within ${\sim}2.5{\sigma}$. The mean velocity ($<v_p>=-342{\pm}60km/s$) of 33 blue GCs in M86 is similar to that ($<v_p>=-314{\pm}71km/s$) of 23 red GCs. We also derive the mean velocities of the GC systems in other 16 nearby early-type galaxies (ETGs) from the radial velocity data in the literature. The mean value of the differences between the mean velocity of the GC systems in each galaxy and the nucleus velocity of their host galaxies, is almost zero except the M86 GC system. But the scatter of the differences in the blue GC system is larger than that in the red GC system. We will discuss these results in the context of GC formation in ETGs.