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A class of distributions with the linear mean residual quantile function and it’s generalizations
Institution:1. Department of Statistics and Biostatistics, Rutgers University, Piscataway, NJ 08854, USA;2. Department of Biostatistics, Yale University, School of Public Health, New Haven, CT 06511, USA;3. Independent Consultant, Sudbury, MA 01776, USA;1. Operations Research Center, Massachusetts Institute of Technology, United States;2. Electric Power Optimization Centre, The University of Auckland, New Zealand;1. Institute of Statistical Science, Academia Sinica, Taipei, Taiwan;2. Institute of Fundamental Sciences–Statistics & Bioinformatics, Massey University, Palmerston North, New Zealand;1. Department of Mechanical Engineering and Aeronautics, University of Patras, Rio, Patras 26500, Greece;2. Applied Mathematics Laboratory, University of Technology of Compiegne, France;3. ALSTOM Transport, Paris, France;1. Department of Civil and Environmental Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada;2. Ontario Power Generation, 889 Brock Road, Pickering, Ontario L1W 3J2, Canada
Abstract:In the present paper, we introduce and study a class of distributions that has the linear mean residual quantile function. Various distributional properties and reliability characteristics of the class are studied. Some characterizations of the class of distributions are presented. We then present generalizations of this class of distributions using the relationship between various quantile based reliability measures. The method of L-moments is employed to estimate parameters of the class of distributions. Finally, we apply the proposed class of distributions to a real data set.
Keywords:Quantile function  Quantile density function  Linear mean residual quantile function  L-moments
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