We introduce a new extension of the Fréchet distribution for modeling extreme values. The model generalizes eleven distributions at least, five them are quite new. Some important mathematical properties derived. assess performance maximum likelihood estimators (MLEs) via simulation study. is better than some other competitive models in breaking stress data, glass fibers data and relief time data.

We prove that the non-vanishing conjecture holds for generalized lc pairs with a polarization.

In this paper, we discuss the properties of the hyperfibonacci numbers F [r] n and hyperlucas numbers L [r] n . We investigate the log-concavity (log-convexity) of hyperfibonacci numbers and hyperlucas numbers. For example, we prove that {F [r] n }n≥1 is log-concave. In addition, we also study the log-concavity (log-convexity) of generalized hyperfibonacci numbers and hyperlucas numbers.