Use draw9patch... included within Android Studio's SDK tools. You can define the stretchable areas of your image. Important parts are constrained and the image doesn't look all warped. A good demo on dra9patch is HERE
Use draw9patch to change your existing splash.png into new_splash.9.png, drag new_splash.9.png into the drawable-hdpi project folder ensure the AndroidManifest and styles.xml are proper as below:
AndroidManifest.xml:
<application
...
android:theme="@style/splashScreenStyle"
>
styles.xml:
<style name="splashScreenStyle" parent="Theme.AppCompat.Light.DarkActionBar">
<item name="android:windowBackground">@drawable/new_splash</item>
</style>