## 1 Introduction  
Lifetime models are a probability distribution with either a non-negative or positive support which are considered in survival analysis. In the literature, there exist many well-known life models, including, but not limited to, the exponential distribution and its generalization; the Weibull distribution. The main limitation of these two models is that they are not suitable for data with non-monotonic hazard rates. Examples of non-monotonic hazard rates are the bathtub and the upside-down hazard rates. From a medical perspective, the bathtub hazard rate represents three life phases. The first phase is called the infant mortality period which is a duration of time with decreasing hazard rate. The second part is the normal life period in which a constant hazard rate is maintained. The final phase is a period of time in which the hazard rate increases due to aging. Additionally, the upside-down hazard rate can be considered to describe the behavior of malicious diseases, such as cancer. In fact, ref. [1] observed such a hazard rate in the case of a certain type of breast cancer. They concluded that the mortality (i.e., hazard) rate increased to its highest peak which was approximately three years after the cancer was diagnosed. Afterwards, they observed that over a specified amount of time, the mortality rate decreases slowly. In the literature, skewed life distributions such as the inverse Gaussian, the log-Gaussian, and the Birnbaum-Saunders distribution have been used to model phenomena with an upside-down hazard rate [2]. The latter model, however, received considerable attention from many researchers due to its desirable properties and physical interpretation. In fact, at least 200 articles and a single study monograph have previously been published detailing many aspects and advancements connected to this lifetime model. For more details, see [2]. The Birnbaum-Saunders (BS) distribution [3, 4] belongs to a generalized BS (GBS) distribution, which was presented by [5] and later discussed by [6, 7]. Researchers today deal with a variety of types and huge amounts of data from different fields, due to recent developments in applied sciences. In practice, there's no guarantee that these data are free of contamination, such as outliers, since contamination might originate from a variety of sources. Accordingly, estimation efficiency may be affected by this contamination. Therefore, the pollution aspect in data has motivated many researchers to suggest alternative estimators to those derived by the maximum likelihood theory for many distributions; see, for example, [8; 9; 10; 11; 12], among other papers. This paper's aim is to study a specific instance of the GBS distribution; namely, the BS distribution established on a logistic kernel [13]. The considered model will henceforth be called the Logistic BS (LBS) distribution. The LBS distribution is considered for several reasons: the first is to investigate the behavior of LBS distribution compared to BS distribution in terms of distribution properties such as hazard (failure rate) function (HF). The second is to compare the application of LBS distribution to BS and other well-known distributions by analyzing two real-life medical datasets. Alongside these reasons, we are going to study the properties of the distribution and derive estimators for the model parameters using two estimation methods. Although the LBS distribution was considered previously by [14], this study differs from the latter contribution in a few points. First and foremost, the latter contribution pointed out that the hazard rate has a single nonmonotonic shape (i.e., inverse bathtub shape), while our study indicates that the hazard rate has two forms as shown in a later section. Second, while both [14] and this study derived similar statistical properties (e.g., mean, median, etc. ), we have discussed some distributional aspects of the LBS distribution such as the corresponding mean residual life of the LBS distribution as well as the distribution of order statistics.