On Square Logistic Distribution: Mathematical Properties, Estimation Methods and Applications in Biology

Abstract

In the current investigation, we formulate and analyze the Square–Logistic distribution (SLD), which is developed by integrating the half–logistic and odd Fréchet–G families. The SLD exhibits highly versatile probability functions: it encompasses hazard rate functions that are decreasing, increasing, exhibit a bathtub shape, and an inverted U shape, thereby demonstrating the model’s inherent flexibility. A thorough examination of the mathematical and statistical characteristics of the proposed model is provided. From an estimation perspective, different methodologies are employed to estimate the unknown parameter(s) of the SLD. In addition, an extensive Monte Carlo simulation study is conducted to assess the effectiveness of these estimators. Lastly, real data applications are employed to illustrate the adaptability of the proposed method, with comparisons drawn against the half–logistic and some of its prominent extensions.