References
- Aarset, M. V. (1987). How to identify a bathtub hazard rate. IEEE Transactions on Reliability, 36(1): 106–108.
- Adamidis, K. and Loukas, S. (1998). A lifetime distribution with decreasing failure rate. Statistics & Probability Letters, 39(1): 35–42.
- Anatolyev, S. and Kosenok, G. (2005). An alternative to maximum likelihood based on spacings. Econ Theory, 21(2): 472–476.
- Barlow, R. E., Marshall, A. W., and Proschan, F. (1963). Properties of probability distributions with monotone hazard rate. The Annals of Mathematical Statistics, 34(2): 375–389.
- Barlow, R. E. and Proschan, F. (1975). Statistical theory of reliability and life testing: probability models. Technical report, Florida State Univ Tallahassee.
- Barndorff-Nielsen, O. (1977). Exponentially decreasing distributions for the logarithm of particle size. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, volume 353, pages 401–419.
- Bennett, S. (1983). Log-logistic regression models for survival data. Applied Statistics, 32(2): 165–171.
- Bickel, P. J. and Lehmann, E. L. (1975). Descriptive statistics for non-parametric models ii location. The Annals of Statistics, 3(5): 1045–1069.
- Birnbaum, Z. (1948). On random variables with comparable peakedness. The Annals of Mathematical Statistics, 19(1): 76–81.
- Boos, D. D. (1981). Minimum distance estimators for location and goodness of fit. Journal of the American Statistical association, 76(375): 663–670.
- Bowley, A. L. (1920). Elements of statistics, volume 2. PS King.
- Chahkandi, M. and Ganjali, M. (2009). On some lifetime distributions with decreasing failure rate. Computational Statistics & Data Analysis, 53(12): 4433–4440.
- Cheng, R. C. H. and Amin, N. A. K. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society. Series B (Methodological), 45(3): 394–403.
- Choi, K. and Bulgren, W. G. (1968). An estimation procedure for mixtures of distributions. Journal of the Royal Statistical Society. Series B (Methodological), 30(3): 444–460.
- Coolen, F. P. A. and Newby, M. J. (1990). A note on the use of the product of spacings in Bayesian inference. Department of Mathematics and Computing Science, Eindhoven University of Technology.
- De Gusm∼ao, F. R. S., Ortega, E. M. M., and Cordeiro, G. M. (2011). The generalized inverse Weibull distribution. Statistical Papers, 52(3): 591–619.
- Deshpande, J. V. and Purohit, S. G. (2005). Lifetime Data: Statistical Models and Methods. World Scientific.
- Deshpande, J. V. and Suresh, R. P. (1990). Non-monotonic ageing. Scandinavian journal of statistics, 17(3): 257–262.
- Efron, B. (1982). The jackknife, the bootstrap, and other resampling plans, volume 38. Siam.
- Efron, B. (1988). Logistic regression, survival analysis, and the kaplan-meier curve. Journal of the American statistical Association, 83(402): 414–425.
- Foss, S., Korshunov, D., and Zachary, S. (2011). An introduction to heavy-tailed and subexponential distributions, volume 6. Springer.
- Glaser, R. E. (1980). Bathtub and related failure rate characterizations. Journal of the American Statistical Association, 75(371): 667–672.
- Gobbi, F. (2018). Tail behavior of a sum of two dependent and heavytailed distributions. Journal of Statistics and Management Systems, 21(6): 933–953.
- Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical transactions of the Royal Society of London, 115: 513–583.
- Gupta, R. C., Gupta, P. L., and Gupta, R. D. (1998). Modeling failure time data by lehmann alternatives. Communications in Statistics-Theory and Methods, 27(4): 887–904.
- Gupta, R. D. and Kundu, D. (2001). Generalized exponential distribution: different method of estimations. Journal of Statistical Computation and Simulation, 69(4): 315–337.
- Hall, P. (1988). Theoretical comparison of bootstrap confidence intervals. The Annals of Statistics, 16(3): 927–953.
- Hjorth, U. (1980). A reliability distribution with increasing, decreasing, constant and bathtub-shaped failure rates. Technometrics, 22(1): 99–107.
- Hubert, M. and Vandervieren, E. (2008). An adjusted boxplot for skewed distributions. Computational Statistics and Data Analysis, 52: 51865201.
- Johnson, N. L, K. S. and Balakrishnan, N. (1994). In Continious Univariate Distributions, volume 2. John Wiley & Sons.
- Khan, M. S., King, R., and Hudson, I. (2014). Characterizations of the transmuted inverse Weibull distribution. ANZIAM Journal, 55(EMAC2013): 197–217.
- Klugman, S. A., Panjer, H. H., and Willmot, G. E. (2012). Loss models: from data to decisions, volume 715. John Wiley & Sons.
- Kuş, C. (2007). A new lifetime distribution. Computational Statistics & Data Analysis, 51(9): 4497–4509.
- Lamberson, L. R. (1974). An evaluation and comparison of some tests for the validity of the assumption that the underlying distribution of life is exponential. AIIE Transactions, 6(4): 327-337.
- Lehmann, E. L. (1955). Ordered families of distributions. The Annals of Mathematical Statistics, 26(3): 399–419.
- Leiva, V., Athayde, E., Azevedo, C., and Marchant, C. (2011). Modeling wind energy flux by a birnbaum-saunders distribution with an unknown shift parameter. Journal of Applied Statistics, 38(12): 2819– 2838.
- MacDonald, P. D. M. (1971). Comment on “an estimation procedure for mixtures of Distributions” by Choi and Bulgren. Journal of the Royal Statistical Society. Series B (Methodological), 33(2): 326–329.
- Mann, H. B. and Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. The annals of mathematical statistics, 18(1): 50–60.
- Marshall, A. W. and Olkin, I. (1988). Families of multivariate distributions. Journal of the American statistical association, 83(403): 834–841.
- Marshall, A. W. and Olkin, I. (2007). Life distributions, volume 13. Springer.
- Marshall, A. W., Olkin, I., and Arnold, B. C. (1979). Inequalities: theory of majorization and its applications, volume 143. Springer.
- Maurya, S. K., Kumar, D., Singh, S. K., and Singh, U. (2018). One parameter decreasing failure rate distribution. International Journal of Statistics & Economics, 19(1): 120–138.
- Moors, J. J. A. (1988). A quantile alternative for kurtosis. The statistician, 37(1): 25–32.
- Mudholkar, G. S. and Srivastava, D. K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability, 42(2): 299–302.
- Müller, A. and Stoyan, D. (2002). Comparison methods for stochastic models and risks, volume 389. Wiley.
- Nair, J., Wierman, A., and Zwart, B. (2013). The fundamentals of heavy-tails: properties, emergence, and identifocation. In ACM SIGMETRICS Performance Evaluation Review, volume 41, pages 387–388.
- Oguntunde, P. and Adejumo, O. (2014). The transmuted inverse exponential distribution. International Journal of Advanced Statistics and Probability, 3(1): 1–7.
- Pitman, E. J. (1937). The closest estimates of statistical parameters. In MathematicalProceedings of the Cambridge Philosophical Society, volume 33, pages 212–222.
- Proschan, F. (1963). Theoretical explanation of observed decreasing failure rate. Tech-nometrics, 5(3): 375–383.
- R Core Team (2019). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
- Rajarshi, S. and Rajarshi, M. B. (1988). Bathtub distributions: A review. Communications in Statistics-Theory and Methods, 17(8): 2597– 2621.
- Ranneby, B. (1984). The maximum spacing method. an estimation method related to the maximum likelihood method. Scandinavian Journal of Statistics, 11(2): 93–112.
- Shanker, R., Hagos, F., and Sujatha, S. (2015). On modeling of lifetimes data using exponential and Lindley distributions. Biometrics and Biostatistics International Journal, 2(5): 1–9.
- Shannon, C. E. (1951). Prediction and entropy of printed english. The Bell System Technical Journal, 30(1): 50–64.
- Sharma, V. K., Singh, S. K., and Singh, U. (2014). A new upside-down bathtub shaped hazard rate model for survival data analysis. Applied Mathematics and Computation, 239(2014): 242–253.
- Sharma, V. K., Singh, S. K., Singh, U., and Agiwal, V. (2015). The inverse Lindley distribution: a stress-strength reliability model with application to head and neck cancer data. Journal of Industrial and Production Engineering, 32(3): 162–173.
- Sharma, V. K., Singh, S. K., Singh, U., and Merovci, F. (2016). The generalized inverse Lindley distribution: A new inverse statistical model for the study of upside-down bathtub data. Communications in Statistics-Theory and Methods, 45(19): 5709–5729.
- Shaw, W. T. and Buckley, I. R. C. (2007). The alchemy of probability distributions: beyond gram-charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. arXiv preprint arXiv: 0901.0434.
- Singh, R. K., Yadav, A. S., Singh, S. K., and Singh, U. (2016). Marshallolkin extended exponential distribution: Different method of estimations. Journal of Advanced Computing, 5(1): 12–28.
- Singh, U., Singh, S. K., and Singh, R. K. (2014a). A comparative study of traditional estimation methods and maximum product spacings method in generalized inverted exponential distribution. Journal of Statistics Applications & Probability, 3(2): 153–169.
- Singh, U., Singh, S. K., and Singh, R. K. (2014b). Product spacings as an alternative to likelihood for Bayesian inferences. Journal of Statistics Applications & Probability, 3(2): 179–188.
- Swain, J. J., Venkatraman, S., and Wilson, J. R. (1988). Least-squares estimation of distribution functions in johnson’s translation system. Journal of Statistical Computation and Simulation, 29(4): 271–297.
- Szekli, R. (1995). Stochastic ordering and dependence in applied probability, volume 97. Springer Science & Business Media.
- Tahmasbi, R. and Rezaei, S. (2008). A two-parameter lifetime distribution with decreasing failure rate. Computational Statistics & Data Analysis, 52(8): 3889–3901.
- Weibull, W. (1951). A statistical distribution of wide applicability. Journal of applied mechanics, 103(730): 293–297.
- Xie, M. and Lai, C. D. (1996). Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function. Reliability Engineering & System Safety, 52(1): 87–93.
- Xie, M., Tang, Y., and Goh, T. N. (2002). A modi_ed Weibull extension with bathtubshaped failure rate function. Reliability Engineering & System Safety, 76(3): 279–285.
- Yadav, A. S. (2019). The inverted exponentiated gamma distribution: A heavy-tailed model with upside down bathtub shaped hazard rate. Statistica, 79(3): 339–360.