On the monotonic properties of discrete failure rates |
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| Institution: | 1. Department of Mathematics and Statistics, University of Maine, Orono, Maine 04469-5752, USA;2. Division of Mathematics and Statistics, University of Texas at San Antonio, San Antonio, TX 78249, USA;1. Faculty of Electrical Engineering and Computer Science, Ningbo University, Ningbo 315211, China;2. Department of Information Science and Electronics Engineering and Cyrus Tang Center for Sensor Materials and Applications, Zhejiang University, Hangzhou 310027, China;1. Beijing Centre for Disease Prevention and Control (CDC), No. 16 He Pingli Middle St, Dongcheng District, Beijing 100013, China;2. School of Public Health and Western College of Veterinary Medicine, University of Saskatchewan, Saskatoon, Canada;3. School of Environment and Sustainability, University of Saskatchewan, Saskatoon, Canada;4. Tulane Infectious Disease Department, Tulane University, New Orleans, Louisiana, USA;5. School of Public Health and Tropical Medicine, Tulane University, 1440 Canal Street, Suite 2100, New Orleans, LA 70112, USA;1. Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India;2. Bhai Mani Singh Polytechnic, Bathinda, Punjab, India;3. Institute of Materials Science, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Viet Nam;4. University of Science and Technology of Hanoi, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Viet Nam |
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| Abstract: | As is well known, the monotonicity of failure rate of a life distribution plays an important role in modeling failure time data. In this paper, we develop techniques for the determination of increasing failure rate (IFR) and decreasing failure rate (DFR) property for a wide class of discrete distributions. Instead of using the failure rate, we make use of the ratio of two consecutive probabilities. The method developed is applied to various well known families of discrete distributions which include the binomial, negative binomial and Poisson distributions as special cases. Finally, a formula is presented to determine explicitly the failure rate of the families considered. This formula is used to determine the failure rate of various classes of discrete distributions. These formulas are explicit but complicated and cannot normally be used to determine the monotonicity of the failure rates. |
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