The main purpose of this paper is to present k-Generalized Exponential Distribution which among other things includes Generalized Exponential and Weibull Distributions as special cases. Besides, we also obtain three-parameter extension of Generalized Exponential Distribution. We shall also discuss moment generating functions (MGFs) of these newly introduced distributions.

No abstract

In this paper, we first prove a theorem which gives considerably better bound for 0 ≤ t ≤ 1/2 than Gaussian tail inequality (or tail bound for normal density) and thus is a refinement of Gaussian tail inequality in this case. Next we present an interesting result which provides a refinement of Gaussian tail inequality for t > √ 3. Besides, we also prove an improvement of Gaussian tail inequality for 0 < t ≤ 1/2. Finally, we present a more general result which includes a variety of interesting results as special cases.

No abstract